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math Mathematics

All areas of pure and applied mathematics.

Categories

AC Commutative Algebra 1
AG Algebraic Geometry 24
AP Analysis of PDEs 188
AT Algebraic Topology 23
CA Classical Analysis and ODEs 11
CO Combinatorics 100
CT Category Theory —
CV Complex Variables —
DG Differential Geometry 25
DS Dynamical Systems 32
FA Functional Analysis 45
GM General Mathematics —
GN General Topology —
GR Group Theory 3
GT Geometric Topology 6
HO History and Overview —
IT Information Theory 12
KT K-Theory and Homology —
LO Logic —
MG Metric Geometry 35
MP Mathematical Physics 19
NA Numerical Analysis 138
NT Number Theory 54
OA Operator Algebras 22
OC Optimization and Control 39
PR Probability 114
QA Quantum Algebra —
RA Rings and Algebras 2
RT Representation Theory —
SG Symplectic Geometry 2
SP Spectral Theory 68
ST Statistics Theory 17

Papers claiming problems in math

Problems

OP-00001 Open
Goldbach's conjecture
NT · additive prime number theory · Landau's problems
OP-00002 Open
The twin prime conjecture
NT · Landau's problems · prime gaps
OP-00003 Open
Legendre's conjecture
NT · Landau's problems · prime gaps
OP-00004 Open
Primes of the form n² + 1
NT · Landau's problems · primes represented by polynomials
OP-00005 Open
The odd perfect number conjecture
NT · perfect numbers · sum of divisors
OP-00006 Open
Lehmer's totient problem
NT · Euler's totient function
OP-00007 Open
The Kummer–Vandiver conjecture
NT · class numbers · cyclotomic fields
OP-00008 Open
Pillai's conjecture on axⁿ − byᵐ = c
NT · exponential Diophantine equations · perfect powers
OP-00009 Open
The Feit–Thompson conjecture on primes
NT · divisibility
OP-00010 Open
The Lander–Parkin–Selfridge conjecture
NT · Diophantine equations · equal sums of like powers
OP-00011 Open
A 3 × 3 magic square of distinct squares
NT · Diophantine equations · magic squares
OP-00012 Open
Schanuel's conjecture
NT · exponential function · transcendental numbers
OP-00013 Open
The four exponentials conjecture
NT · exponential function · transcendental numbers
OP-00014 Open
Irrationality of the Euler–Mascheroni constant
NT · Euler–Mascheroni constant · irrationality
OP-00015 Solution claimed
Convergence of the Flint Hills series
CA · irrationality measure · series convergence
OP-00016 Solution claimed
Falconer's distance set conjecture
CA · distance sets · geometric measure theory · Hausdorff dimension
OP-00017 Partially resolved
The Marcus–de Oliveira determinantal conjecture
RA · determinants · normal matrices
OP-00018 Open
The 1/3–2/3 conjecture for finite posets
CO · linear extensions · partially ordered sets · sorting
OP-00019 Open
The prime power conjecture for finite projective planes
CO · Erdős problems · finite projective planes
OP-00020 Solution claimed
The Gaussian moat problem
NT · Erdős problems · Gaussian primes
OP-00021 Open
Interior of the spectrum of the boat–star tiling Laplacian
SP · aperiodic order · Cantor spectrum · graph Laplacian · Penrose tiling
OP-00022 Open
Intervals of spectrum at the edges of the boat–star tiling spectrum
SP · aperiodic order · graph Laplacian · Penrose tiling · spectral edges
OP-00023 Open
Closed form for the top of the boat–star tiling spectrum
SP · aperiodic order · graph Laplacian · Penrose tiling · spectral edges
OP-00024 Open
Tilings without locally supported eigenfunctions in every MLD class
SP · aperiodic order · graph Laplacian · locally supported eigenfunctions · mutual local derivability
OP-00025 Open
Finitely many jumps in the integrated density of states of a linearly repetitive tiling
SP · aperiodic order · graph Laplacian · integrated density of states · linear repetitivity · locally supported eigenfunctions
OP-00026 Open
Hölder continuity of the boat–star integrated density of states at the spectral edges
SP · aperiodic order · Hölder continuity · integrated density of states · Penrose tiling · spectral edges
OP-00027 Open
Interior, edge intervals and edge regularity for the Robinson triangle tiling Laplacian
SP · Cantor spectrum · graph Laplacian · integrated density of states · Penrose tiling · Robinson triangles
OP-00028 Open
Spectral gaps of the Robinson triangle tiling Laplacian
SP · Cantor spectrum · graph Laplacian · Penrose tiling · Robinson triangles · spectral gap
OP-00029 Solution claimed
Global synchronization of random 3-regular graphs
PR · global synchronization · Kuramoto model · random regular graphs · Randomstrasse101
OP-00030 Open
Sub-exponential detection in the hard regime of multi-frequency synchronization
ST · group synchronization · Randomstrasse101 · spiked random matrices · statistical-to-computational gaps
OP-00031 Open
The largest discrepancy of square ±1 matrices relative to √n
CO · discrepancy theory · Randomstrasse101 · sign matrices · Spencer's theorem
OP-00032 Open
The Hadamard conjecture
CO · combinatorial designs · Hadamard matrices · Randomstrasse101
OP-00033 Partially resolved
Fast mixing of Glauber dynamics for the SK model up to β = 1
PR · Glauber dynamics · mixing time · Randomstrasse101 · Sherrington–Kirkpatrick model · spin glasses
OP-00034 Open
A type-2 inequality for injective norms of Gaussian sums of tensors
PR · injective norm · matrix concentration inequalities · Randomstrasse101 · random tensors
OP-00035 Open
The Lovász number of random circulant graphs
CO · circulant graphs · Lovász theta function · random graphs · Randomstrasse101
OP-00036 Partially resolved
Vinzant's conjecture on 4M − 5 phase retrieval measurements
FA · frames · injectivity · phase retrieval · Randomstrasse101
OP-00037 Open
The Balan–Wang conjecture on the stability of real phase retrieval
FA · frames · phase retrieval · Randomstrasse101 · stability
OP-00038 Partially resolved
A degree-4 Sum-of-Squares proof that ℂ⁶ has no seven mutually unbiased bases
OC · mutually unbiased bases · Randomstrasse101 · semidefinite programming · Sum-of-Squares
OP-00039 Solution claimed
Zauner's conjecture
FA · equiangular tight frames · quantum information · Randomstrasse101 · SIC-POVM
OP-00040 Open
The clique number of Paley graphs
NT · clique number · Paley graph · pseudorandom graphs · Randomstrasse101
OP-00041 Open
The Lovász number of the 1-localization of the Paley graph
CO · clique number · Lovász theta function · Paley graph · Randomstrasse101
OP-00042 Open
A Lovász-number bound for the 2-localization of the Paley graph
CO · clique number · Lovász theta function · Paley graph · Randomstrasse101
OP-00043 Open
A degree-4 Sum-of-Squares bound for the Paley clique number
OC · clique number · Paley graph · Randomstrasse101 · Sum-of-Squares
OP-00044 Open
The Paley ETF restricted isometry conjecture
FA · compressed sensing · equiangular tight frames · Paley graph · Randomstrasse101 · restricted isometry property
OP-00045 Solution claimed
The Kannan–Lovász–Simonovits conjecture
PR · convex geometry · isoperimetry · KLS conjecture · log-concave measures · Randomstrasse101
OP-00046 Open
Minimum and maximum bisections of random regular graphs
PR · graph bisection · maximum cut · random regular graphs · Randomstrasse101 · spin glasses
OP-00047 Open
Directional convex hulls that are not semialgebraic
MG · directional convexity · Randomstrasse101 · rank-one convexity · semialgebraic sets
OP-00048 Open
When are directional convex hulls semialgebraic?
MG · directional convexity · Randomstrasse101 · rank-one convexity · semialgebraic sets
OP-00049 Open
Rigorous consequences of low-degree hardness
ST · hypothesis testing · low-degree polynomials · Randomstrasse101 · statistical-to-computational gaps
OP-00050 Open
A low-degree polynomial that finds cliques of size log₂ n in G(n, 1/2)
PR · clique number · low-degree polynomials · random graphs · Randomstrasse101
OP-00051 Solution claimed
The Group Spencer conjecture
CO · discrepancy theory · Matrix Spencer · Randomstrasse101 · regular representation
OP-00052 Solution claimed
Global synchronization with negative edges
PR · Burer–Monteiro · community detection · global synchronization · Kuramoto model · Randomstrasse101
OP-00053 Solution claimed
The minimum-degree threshold 3/4 for global synchronization
CO · extremal graph theory · global synchronization · Kuramoto model · Randomstrasse101
OP-00054 Solution claimed
The spectral threshold of Kikuchi matrices for tensor PCA
PR · Kikuchi hierarchy · random matrices · Randomstrasse101 · statistical-to-computational gaps · tensor PCA
OP-00055 Solution claimed
Infinitely many square ±1 matrices with discrepancy a constant factor above √n
CO · discrepancy theory · Randomstrasse101 · sign matrices · Spencer's theorem
OP-00056 Solved
The discrepancy of the Sylvester–Hadamard matrices H_k for odd k
CO · Boolean functions · discrepancy theory · Hadamard matrices · Randomstrasse101
OP-00057 Solution claimed
The Lovász number of G(n, 1/2)
CO · Lovász theta function · random graphs · Randomstrasse101 · semidefinite programming
OP-00058 Solution claimed
Maximum cut and maximum bisection of random regular graphs
PR · graph bisection · maximum cut · random regular graphs · Randomstrasse101
OP-00059 Solution claimed
Sharp norm bounds for graph matrices
PR · graph matrices · matrix chaos · random matrices · Randomstrasse101 · Sum-of-Squares
OP-00060 Solution claimed
The value of ω(A) for Gaussian matrices in real phase retrieval
PR · phase retrieval · random matrices · Randomstrasse101 · stability
OP-00061 Solution claimed
The Matrix Spencer conjecture
CO · discrepancy theory · Matrix Spencer · random matrices · Randomstrasse101
OP-00062 Solution claimed
Fitting ellipsoids to random points: the threshold d²/4
PR · ellipsoid fitting · phase transitions · random geometry · Randomstrasse101 · semidefinite programming
OP-00063 Solution claimed
A diverging number of frequencies in multi-frequency synchronization
ST · group synchronization · Randomstrasse101 · spiked random matrices · statistical-to-computational gaps
OP-00064 Solution claimed
The Komlós conjecture
CO · discrepancy theory · Komlós conjecture · Randomstrasse101 · vector balancing
OP-00065 Open
A critical number of frequencies for weak recovery in multi-frequency synchronization
ST · group synchronization · low-degree polynomials · spiked random matrices · statistical-to-computational gaps
OP-00066 Partially resolved
Is the matrix multiplication exponent two?
NA · arithmetic complexity · matrix multiplication · OpenProblemsInNLA
OP-00067 Open
Border rank of the 3×3 matrix product
AG · border rank · matrix multiplication · OpenProblemsInNLA · tensor rank
OP-00068 Open
Strassen's asymptotic rank conjecture for tight tensors
AG · asymptotic rank · matrix multiplication · OpenProblemsInNLA · tensor rank
OP-00069 Open
Knuth–Stolarsky lower bound for addition chains
NT · addition chains · exponentiation · OpenProblemsInNLA
OP-00070 Open
An explicit rational Valiant-rigid matrix family
CO · circuit lower bounds · matrix rigidity · OpenProblemsInNLA
OP-00071 Open
Audenaert's two-row Schatten norm-compression conjecture
FA · block matrices · norm inequalities · OpenProblemsInNLA · Schatten norms
OP-00072 Partially resolved
Minimum number of orthogonal conjugations for diagonal pinching
FA · OpenProblemsInNLA · orthogonal matrices · pinching
OP-00073 Open
Chollet's permanent inequality for Hadamard products
FA · Hadamard product · OpenProblemsInNLA · permanents
OP-00074 Open
Lieb's permanental dominance conjecture
FA · generalized matrix functions · immanants · OpenProblemsInNLA · permanents
OP-00075 Solution claimed
No seven mutually unbiased bases in ℂ⁶
CO · frames · mutually unbiased bases · quantum information · Randomstrasse101
OP-00076 Lean verified
Counting real Hadamard matrices
CO · Hadamard matrices · OpenProblemsInNLA · sign matrices
OP-00077 Lean verified
Is the ideal GMRES bound sharp for every Jordan block?
NA · GMRES · Jordan blocks · Krylov subspace methods · OpenProblemsInNLA
OP-00078 Lean verified
Exponential smoothed tail bounds for partial pivoting
NA · Gaussian elimination · growth factors · OpenProblemsInNLA · smoothed analysis
OP-00079 Lean verified
Exact extremizers for partial pivoting on orthogonal matrices
NA · Gaussian elimination · growth factors · OpenProblemsInNLA · orthogonal matrices
OP-00080 Lean verified
A sharp subset bound for worst-case normal GMRES
NA · GMRES · normal matrices · OpenProblemsInNLA · polynomial approximation
OP-00081 Lean verified
Monotonic optimal backward error along LSMR
NA · backward errors · least-squares problems · LSMR · OpenProblemsInNLA
OP-00082 Lean verified
The exact four-step amplification of restarted Anderson acceleration
NA · Anderson acceleration · convergence factors · fixed-point iterations · OpenProblemsInNLA
OP-00083 Lean verified
Sharp inverse norm bound from upper bounds on matrix entries
NA · diagonally dominant matrices · matrix inverses · OpenProblemsInNLA
OP-00084 Lean verified
Uniqueness of the right inverse minimizing an induced p-to-2 norm
NA · generalized inverses · induced norms · OpenProblemsInNLA
OP-00085 Lean verified
Where a symmetric stochastic matrix can be spectrally unique
NA · doubly stochastic matrices · inverse eigenvalue problems · OpenProblemsInNLA
OP-00086 Lean verified
Johnson's derivative-realizability conjecture
NA · critical points · inverse eigenvalue problems · nonnegative matrices · OpenProblemsInNLA
OP-00087 Lean verified
Polynomial-size vertex test for inverse M-matrix intervals
NA · interval matrices · inverse M-matrices · OpenProblemsInNLA
OP-00088 Lean verified
Number of components of a real interval eigenvalue set
NA · interval matrices · OpenProblemsInNLA · real eigenvalues
OP-00089 Lean verified
Strict interlacing across block Lanczos iterations
NA · block Lanczos methods · eigenvalue interlacing · OpenProblemsInNLA · Ritz values
OP-00090 Lean verified
Local Hölder continuity of the joint spectral radius
DS · Hölder continuity · joint spectral radius · OpenProblemsInNLA
OP-00091 Lean verified
A pointwise Lipschitz lower bound for the joint spectral radius
DS · joint spectral radius · OpenProblemsInNLA · perturbation bounds
OP-00092 Lean verified
Uniform polynomial bounds for products at joint spectral radius one
DS · joint spectral radius · matrix products · OpenProblemsInNLA
OP-00093 Lean verified
Realizing arbitrary polynomial growth exponents by finite matrix families
DS · growth rates · joint spectral radius · matrix products · OpenProblemsInNLA
OP-00094 Lean verified
Degree coverage with seven matrix multiplications
NA · matrix multiplication · matrix polynomials · OpenProblemsInNLA
OP-00095 Lean verified
Imaginary-part rank in a limiting Green-function matrix equation
NA · Green's functions · nonlinear matrix equations · OpenProblemsInNLA · quadratic eigenvalue problems
OP-00096 Lean verified
The uniform expansion threshold for Toeplitz symbols with higher-order zeros
NA · eigenvalue asymptotics · OpenProblemsInNLA · Toeplitz matrices
OP-00097 Lean verified
Polynomial conditioning of the cubic C1 spline Schrödinger Toeplitz family
NA · block Toeplitz matrices · condition numbers · isogeometric analysis · OpenProblemsInNLA
OP-00098 Lean verified
Sharp additive triangle constant for an odd number of contractions
FA · contractions · OpenProblemsInNLA · triangle inequalities
OP-00099 Lean verified
A universal block-norm characterization of essentially Hermitian matrices
FA · block matrices · numerical ranges · OpenProblemsInNLA
OP-00100 Lean verified
Thompson-type domination for the arithmetic symmetric modulus
FA · OpenProblemsInNLA · symmetric moduli · triangle inequalities · unitary orbits
OP-00101 Lean verified
The triangle conjecture for the maximal symmetric modulus
FA · OpenProblemsInNLA · spectral order · symmetric moduli · triangle inequalities
OP-00102 Lean verified
Nobori's spectral-middle-factor commutator conjecture
FA · Böttcher–Wenzel inequality · commutators · norm inequalities · OpenProblemsInNLA
OP-00103 Lean verified
A q-permanent inequality for subset-preserving permutations
FA · OpenProblemsInNLA · permanents · q-permanents
OP-00104 Lean verified
Freewan–Hayajneh inequality for sums of weighted geometric means
FA · matrix geometric means · OpenProblemsInNLA · unitarily invariant norms
OP-00105 Lean verified
Lemos–Soares singular-value log-majorization
FA · log-majorization · matrix geometric means · OpenProblemsInNLA · singular values
OP-00106 Lean verified
Corrected generalized geometric-mean product conjecture
FA · eigenvalues · log-majorization · matrix geometric means · OpenProblemsInNLA
OP-00107 Lean verified
Concave unitary-orbit subadditivity without monotonicity
FA · concave functions · matrix subadditivity · OpenProblemsInNLA · unitary orbits
OP-00108 Lean verified
Constant one in the logarithmic commutator inequality
FA · commutators · matrix logarithms · OpenProblemsInNLA
OP-00109 Lean verified
Modulus-order determinant comparison with an arbitrary base power
FA · determinantal inequalities · OpenProblemsInNLA · positive definite matrices
OP-00110 Lean verified
The Rowland–Wu polynomial identity for Sinkhorn limits
NA · matrix scaling · OpenProblemsInNLA · Sinkhorn limits
OP-00111 Lean verified
Full nonnegative rank of the quadratic correlation matrix
NA · extended formulations · nonnegative rank · OpenProblemsInNLA · unique-disjointness matrices
OP-00112 Lean verified
The nonnegative rank of the nine-point distance matrix
NA · Euclidean distance matrices · nonnegative rank · OpenProblemsInNLA
OP-00113 Lean verified
Connectedness of minimal positive semidefinite factorization orbits
NA · matrix factorizations · OpenProblemsInNLA · positive semidefinite rank
OP-00114 Lean verified
Rational factors for rational completely positive boundary matrices
NA · completely positive matrices · OpenProblemsInNLA · rational factorizations
OP-00115 Lean verified
Polynomial trace-error factor after exactly the target rank of pivots
NA · low-rank approximations · OpenProblemsInNLA · pivoted Cholesky factorizations
OP-00116 Lean verified
Improve the randomized LU squared-error factor to 2^k
NA · low-rank approximations · OpenProblemsInNLA · pivoted LU factorizations
OP-00117 Lean verified
Convexity of the expected error of volume-sampled column subsets
NA · column subset selection · elementary symmetric polynomials · OpenProblemsInNLA · volume sampling
OP-00118 Lean verified
Critical-point counts for symmetric rank-two approximation with diagonal zeros
AG · Euclidean distance degrees · low-rank approximations · OpenProblemsInNLA · symmetric matrices
OP-00119 Lean verified
The smallest-multiplier rule for nearest unit-absolute-determinant matrices
NA · Euclidean distance degree · matrix nearness problems · OpenProblemsInNLA
OP-00120 Lean verified
Symmetric minimizer for a positive definite Jordan–Kronecker product
NA · Kronecker products · OpenProblemsInNLA · Rayleigh quotients
OP-00121 Lean verified
A real-valued symbol on a Jordan curve and real Toeplitz spectra
SP · OpenProblemsInNLA · real spectra · Toeplitz matrices
OP-00122 Lean verified
Finitely many unitary classes with prescribed shifted singular values
NA · OpenProblemsInNLA · pseudospectra · unitary similarity
OP-00123 Lean verified
Random column subsets of arbitrary fixed-sparsity matrices
PR · OpenProblemsInNLA · smallest singular values · sparse matrices
OP-00124 Lean verified
Nonnegative H-eigenvalue inheritance from odd-order Hankel tensors
NA · Hankel tensors · H-eigenvalues · OpenProblemsInNLA
OP-00125 Open
Infinite mean condition number in every identifiable tensor format
NA · condition numbers · OpenProblemsInNLA · random tensors · tensor decompositions
OP-00126 Open
Subquadratic overparameterization for iterative decomposition of smoothed tensors
NA · alternating least squares · OpenProblemsInNLA · smoothed analysis · tensor decompositions
OP-00127 Open
Border Comon's conjecture over the complex numbers
AG · border ranks · OpenProblemsInNLA · secant varieties · symmetric tensors
OP-00128 Open
Generic identifiability of tensors at strictly subcritical ranks
AG · identifiability · OpenProblemsInNLA · secant varieties · tensor decompositions
OP-00129 Open
Classification of perfect tensor formats with generic unique decomposition
AG · generic ranks · identifiability · OpenProblemsInNLA · tensor decompositions
OP-00130 Open
Monotonicity of the average number of critical rank-one approximations
NA · critical points · OpenProblemsInNLA · random tensors · rank-one approximations
OP-00131 Open
Exact best-rank-one approximation ratios for general tensor formats
NA · OpenProblemsInNLA · orthogonal tensors · rank-one approximations · spectral norms
OP-00132 Open
Discreteness from below of asymptotic tensor rank
AG · asymptotic ranks · OpenProblemsInNLA · tensor ranks
OP-00133 Open
Irreducibility of asymptotic tensor-rank sublevel varieties
AG · asymptotic ranks · irreducible varieties · OpenProblemsInNLA
OP-00134 Open
Degree-five, six, and nine generation of the Salmon tensor ideal
AG · border ranks · OpenProblemsInNLA · phylogenetic invariants · secant varieties
OP-00135 Open
Cohen–Macaulay coordinate rings for every tensor border-rank variety
AG · Cohen–Macaulay rings · OpenProblemsInNLA · secant varieties · Segre varieties
OP-00136 Open
Entropy formula for the asymptotic subrank of Dicke tensors
CO · asymptotic subranks · Dicke tensors · OpenProblemsInNLA
OP-00137 Partially resolved
Exact partially symmetric rank of products of generalized W tensors
AG · OpenProblemsInNLA · partially symmetric ranks · W-states
OP-00138 Open
Dimension of tensor loci with prescribed minimum border subrank
AG · border subranks · OpenProblemsInNLA · tensor degenerations
OP-00139 Open
The four-exception conjecture for alternating tensor border-rank varieties
AG · alternating tensors · Grassmannians · OpenProblemsInNLA · secant varieties
OP-00140 Partially resolved
Sharp Schatten triangle constants for the arithmetic symmetric modulus
FA · OpenProblemsInNLA · Schatten norms · symmetric moduli · triangle inequalities
OP-00141 Open
Marcus's inequality for the permanent of block permanents
FA · block matrices · OpenProblemsInNLA · permanents
OP-00142 Open
The complex Lu–Wenzel spectral conjecture
FA · Böttcher–Wenzel inequality · commutators · eigenvalue inequalities · OpenProblemsInNLA
OP-00143 Open
The Lih–Wang permanent inequality toward the flat matrix
FA · doubly stochastic matrices · OpenProblemsInNLA · permanents
OP-00144 Partially resolved
Sharp subquadratic Lee constants for sums of matrices
FA · matrix absolute values · norm inequalities · OpenProblemsInNLA · Schatten norms
OP-00145 Partially resolved
Dimension-independent Hlawka constants for Schatten norms
FA · Hlawka-type inequalities · norm inequalities · OpenProblemsInNLA · Schatten norms
OP-00146 Open
Product inequality for disjoint principal minors of Wishart matrices
FA · Gaussian product inequality · OpenProblemsInNLA · principal minors · Wishart matrices
OP-00147 Open
Deterministic regularization of the nonsymmetric eigenproblem
NA · deterministic algorithms · eigenvector condition numbers · OpenProblemsInNLA · pseudospectra
OP-00148 Open
Two permutation matrices generate the doubly stochastic spectral boundary
NA · doubly stochastic matrices · inverse eigenvalue problems · OpenProblemsInNLA · permutation matrices
OP-00149 Partially resolved
A condition number of two for a sign matrix in every dimension
CO · approximate Hadamard matrices · condition numbers · OpenProblemsInNLA · sign matrices
OP-00150 Partially resolved
The optimal decay exponent for the conditioning of sign matrices
CO · approximate Hadamard matrices · condition numbers · OpenProblemsInNLA · sign matrices
OP-00151 Partially resolved
Construct a separating diagonal perturbation in nearly linear time
NA · deterministic algorithms · eigenvalue gaps · OpenProblemsInNLA · tridiagonal matrices
OP-00152 Open
The sharp generic threshold for spectral-subspace rotation
SP · OpenProblemsInNLA · perturbation bounds · self-adjoint operators · spectral subspaces
OP-00153 Open
The sharp off-diagonal threshold for spectral-subspace rotation
SP · off-diagonal perturbations · OpenProblemsInNLA · perturbation bounds · spectral subspaces
OP-00154 Partially resolved
The Euclidean distance degree of the real symplectic group
NA · Euclidean distance degree · matrix nearness problems · OpenProblemsInNLA · symplectic groups
OP-00155 Partially resolved
The sharp spectral-matching constant for normal matrices
NA · normal matrices · OpenProblemsInNLA · perturbation bounds · spectral variation
OP-00156 Partially resolved
Rank-two maximizers of spectral spread on an entry interval
NA · Bohemian matrices · matrix spread · OpenProblemsInNLA
OP-00157 Partially resolved
Unitary-orbit distance under finite block repetition
NA · matrix nearness problems · normal matrices · OpenProblemsInNLA · unitary orbits
OP-00158 Partially resolved
The graph complement conjecture for minimum symmetric rank
CO · graph complements · inverse eigenvalue problems · minimum rank · OpenProblemsInNLA
OP-00159 Solution claimed
Widom's canonical distribution conjecture for Toeplitz eigenvalues
SP · eigenvalue distributions · OpenProblemsInNLA · Toeplitz matrices
OP-00160 Open
Optimal sign approximation with a multiplication budget
NA · matrix polynomials · matrix sign function · OpenProblemsInNLA · polynomial approximation
OP-00161 Open
Finiteness for nonnegative rational matrix families
DS · finiteness property · joint spectral radius · nonnegative matrices · OpenProblemsInNLA
OP-00162 Open
Decidability of strict stability for rational matrix families
DS · decidability · joint spectral radius · OpenProblemsInNLA · switched linear systems
OP-00163 Open
Algebraicity of joint spectral radii from rational input
DS · algebraic numbers · joint spectral radius · OpenProblemsInNLA
OP-00164 Open
Temporal regularity of marginal matrix-product growth
DS · growth rates · joint spectral radius · matrix products · OpenProblemsInNLA
OP-00165 Open
Symmetric maximizers for Lyapunov operators of order six
NA · Lyapunov operators · OpenProblemsInNLA · singular values
OP-00166 Partially resolved
Critical exponent for generalized doubly nonnegative matrices
NA · critical exponents · matrix powers · nonnegative matrices · OpenProblemsInNLA
OP-00167 Open
Decidability of zero hitting by rational matrix powers
NT · decidability · linear recurrence sequences · OpenProblemsInNLA · Skolem problem
OP-00168 Open
Decidability of zero hitting by a matrix exponential
NT · continuous Skolem problem · decidability · exponential polynomials · OpenProblemsInNLA
OP-00169 Partially resolved
Optimal pivot count for RPCholesky trace approximation
NA · low-rank approximations · Nyström approximations · OpenProblemsInNLA · pivoted Cholesky factorizations
OP-00170 Partially resolved
Optimal trace-estimation complexity using Kronecker matrix-vector queries
NA · Kronecker products · OpenProblemsInNLA · query complexity · trace estimation
OP-00171 Partially resolved
Optimal query complexity of spectral rank-k approximation
NA · Krylov subspace methods · low-rank approximations · OpenProblemsInNLA · query complexity
OP-00172 Open
Query complexity from Schatten to spectral norms
NA · low-rank approximations · OpenProblemsInNLA · query complexity · Schatten norms
OP-00173 Open
Super-exponential decay of the zero-permanent probability
PR · anticoncentration · OpenProblemsInNLA · permanents · random matrices
OP-00174 Partially resolved
Minimum linear measurements for uniform recovery of real low-rank matrices
NA · determinantal varieties · linear measurements · low-rank matrix recovery · OpenProblemsInNLA
OP-00175 Partially resolved
The Goreinov–Tyrtyshnikov–Zamarashkin conjecture on square-submatrix inverse norms
NA · column subset selection · OpenProblemsInNLA · pseudoskeleton approximations
OP-00176 Open
Constant-factor HSS approximation in polynomial time
NA · approximation algorithms · hierarchical matrices · HSS matrices · OpenProblemsInNLA
OP-00177 Open
HSS approximation from a number of matvecs independent of depth
NA · HSS matrices · matrix-vector queries · OpenProblemsInNLA · sketching
OP-00178 Partially resolved
Optimal matvec query complexity of HODLR approximation
NA · HODLR matrices · matrix-vector queries · OpenProblemsInNLA · query complexity
OP-00179 Partially resolved
Sharp gap between volume sampling and the worst matrix with a prescribed spectrum
NA · column subset selection · Nyström approximations · OpenProblemsInNLA · volume sampling
OP-00180 Open
Exact bilinear rank of the 3×3 matrix product
AG · bilinear complexity · matrix multiplication · OpenProblemsInNLA · tensor rank
OP-00181 Partially resolved
Minimal asymptotic rank of the small Coppersmith–Winograd tensor
AG · asymptotic rank · Coppersmith–Winograd tensors · matrix multiplication · OpenProblemsInNLA
OP-00182 Open
Explicit tensors with quadratic border rank
AG · border rank · explicit tensors · OpenProblemsInNLA
OP-00183 Open
Scholz–Brauer inequality for multiplication chains
NT · addition chains · exponentiation · OpenProblemsInNLA
OP-00184 Open
Deterministic polynomial-time commutative Edmonds problem
NA · derandomization · OpenProblemsInNLA · polynomial identity testing · symbolic determinants
OP-00185 Partially resolved
The least positive permanent of a sign matrix
CO · OpenProblemsInNLA · permanents · sign matrices
OP-00186 Partially resolved
Realizing every sign-matrix permanent with negative entries confined on or above the diagonal
CO · OpenProblemsInNLA · permanents · sign matrices
OP-00187 Open
Deterministic near-quadratic matrix multiplication verification
NA · derandomization · matrix multiplication · OpenProblemsInNLA
OP-00188 Open
Cryer's Hadamard complete-pivoting conjecture
NA · Gaussian elimination · growth factors · Hadamard matrices · OpenProblemsInNLA
OP-00189 Open
The exact fifth complete-pivoting growth factor
NA · Gaussian elimination · growth factors · OpenProblemsInNLA
OP-00190 Partially resolved
Precision required for conjugate gradients to attain backward accuracy in n steps
NA · backward errors · conjugate gradient methods · OpenProblemsInNLA · rounding errors
OP-00191 Open
RILU conditioning for the Neumann problem on smooth planar domains
NA · condition numbers · incomplete factorizations · OpenProblemsInNLA · preconditioners
OP-00192 Open
Perturbed MILU conditioning for Neumann problems in two and three dimensions
NA · condition numbers · incomplete LU factorizations · OpenProblemsInNLA · preconditioners
OP-00193 Partially resolved
Spectral disk for a Radau stage preconditioner
NA · eigenvalue bounds · OpenProblemsInNLA · preconditioners · Runge–Kutta methods
OP-00194 Partially resolved
Positive diagonal preconditioning with a nilpotent stiff limit
NA · collocation methods · diagonal preconditioners · OpenProblemsInNLA · Runge–Kutta methods
OP-00195 Partially resolved
Exploit spectral outliers without losing input sparsity
NA · OpenProblemsInNLA · randomized algorithms · singular values · sparse linear systems
OP-00196 Partially resolved
Polynomial-time solution under the regularity promise
NA · absolute value equations · linear complementarity problems · OpenProblemsInNLA · P-matrices
OP-00197 Open
Polynomial-time deterministic restricted isometries with nearly linear row count
FA · compressed sensing · explicit constructions · OpenProblemsInNLA · restricted isometry property
OP-00198 Partially resolved
Sharp sample complexity for restricted isometries from the cyclic Fourier matrix
FA · compressed sensing · OpenProblemsInNLA · restricted isometry property · subsampled Fourier matrices
OP-00199 Partially resolved
Complex equiangular tight frames with twice the dimension
FA · conference matrices · equiangular tight frames · line packings · OpenProblemsInNLA
OP-00200 Partially resolved
The minimum number of quadratic measurements for generalized phase retrieval
FA · OpenProblemsInNLA · phase retrieval · projective spaces · quadratic measurements
OP-00201 Partially resolved
Two-vertex certification of nonsingular sign regularity
NA · interval matrices · OpenProblemsInNLA · sign regular matrices · totally nonnegative matrices
OP-00202 Open
Polynomial-time minimum-volume decision under sufficient scattering
NA · minimum-volume factorizations · nonnegative matrix factorizations · OpenProblemsInNLA · promise problems
OP-00203 Partially resolved
Exact nonnegative rank of regular polygon slack matrices
NA · extended formulations · nonnegative rank · OpenProblemsInNLA · regular polygons
OP-00204 Partially resolved
Additivity for Cartesian-product slack matrices
NA · Cartesian products · extended formulations · nonnegative rank · OpenProblemsInNLA
OP-00205 Partially resolved
Exact positive semidefinite rank of subset-intersection matrices
NA · Johnson schemes · OpenProblemsInNLA · positive semidefinite factorizations · positive semidefinite rank
OP-00206 Solution claimed
Optimal dimension for a rerandomized Hadamard embedding
NA · OpenProblemsInNLA · randomized Hadamard transforms · sketching · subspace embeddings
OP-00207 Solution claimed
Improve the worst-case approximation factor for prescribed tensor-train ranks
NA · approximation algorithms · low-rank approximations · OpenProblemsInNLA · tensor-train decompositions
OP-00208 Solution claimed
Finite mean angular condition number for identifiable tensor decomposition
NA · condition numbers · OpenProblemsInNLA · random tensors · tensor decompositions
OP-00209 Solution claimed
Sharp sparsity threshold for injectivity of a random sparse rectangular matrix
PR · OpenProblemsInNLA · smallest singular values · sparse random matrices · subspace injections
OP-00210 Lean verified
Equality of ranks for generic odd-order Hankel tensors
AG · border ranks · Hankel tensors · OpenProblemsInNLA · tensor ranks
OP-00211 Solution claimed
Comon's exact-rank conjecture for Hankel tensors
AG · Hankel tensors · OpenProblemsInNLA · symmetric tensors · tensor ranks
OP-00212 Solution claimed
Frobenius inner products minimize the algebraic complexity of rank-one approximation
AG · Euclidean distance degrees · OpenProblemsInNLA · rank-one approximations · Segre–Veronese varieties
OP-00213 Solution claimed
Rayleigh–Ritz discriminant degrees for rank-one matrices
AG · discriminants · OpenProblemsInNLA · Rayleigh quotients · Segre varieties
OP-00214 Solution claimed
A Seginer theorem for arbitrary independent identically distributed tensor entries
PR · injective norms · OpenProblemsInNLA · random tensors
OP-00215 Solution claimed
Degrees of the two Rayleigh–Ritz discriminant parts for rational normal curves
AG · discriminants · OpenProblemsInNLA · rational normal curves · Rayleigh quotients
OP-00216 Solution claimed
Border-rank deficiency forcing strict submultiplicativity at the tensor square
AG · border ranks · OpenProblemsInNLA · secant varieties · tensor products
OP-00217 Solution claimed
Forsythe's conjecture beyond restart length two
NA · conjugate gradient methods · Krylov subspace methods · OpenProblemsInNLA
OP-00218 Solution claimed
The square-root upper bound for Gaussian partial-pivoting growth
NA · Gaussian elimination · growth factors · OpenProblemsInNLA · random matrices
OP-00219 Solution claimed
A cubic-time Schur algorithm using logarithmic precision
NA · floating-point arithmetic · OpenProblemsInNLA · randomized algorithms · Schur decompositions
OP-00220 Solution claimed
Conditioning of a random Krylov compression of a cyclic shift
NA · circulant matrices · eigenvector condition numbers · Krylov subspaces · OpenProblemsInNLA
OP-00221 Solution claimed
Near-quadratic solution cost at a prescribed backward error
NA · backward errors · linear systems · OpenProblemsInNLA · randomized algorithms
OP-00222 Solution claimed
Sharp growth for unequal lower and upper bandwidths
NA · banded matrices · Gaussian elimination · growth factors · OpenProblemsInNLA
OP-00223 Solution claimed
Sharp growth for cyclic tridiagonal matrices
NA · Gaussian elimination · growth factors · OpenProblemsInNLA · tridiagonal matrices
OP-00224 Solution claimed
Exact small-order growth factors for rook pivoting
NA · Gaussian elimination · growth factors · OpenProblemsInNLA · rook pivoting
OP-00225 Solution claimed
Sharp row-deletion singular-value limit for spherical random matrices
NA · Kaczmarz methods · OpenProblemsInNLA · random matrices · smallest singular values
OP-00226 Solution claimed
Optimal uniform row-deletion singular-value constant
NA · corrupted linear systems · Kaczmarz methods · OpenProblemsInNLA · smallest singular values
OP-00227 Solution claimed
Sharp stability bounds for perturbed Fourier interpolation
NA · Lebesgue constants · nonuniform Fourier matrices · OpenProblemsInNLA · trigonometric interpolation
OP-00228 Solution claimed
Find a near-largest nonnormal eigenvalue using few matrix-vector products
NA · eigenvalue algorithms · nonnormal matrices · OpenProblemsInNLA · query complexity
OP-00229 Solution claimed
Spectral-gap-independent constants for randomized block polynomial interpolation
NA · block Lanczos methods · matrix polynomials · OpenProblemsInNLA · random matrices
OP-00230 Solution claimed
Multiplication overhead of cubic sign compositions
NA · matrix sign function · OpenProblemsInNLA · polynomial approximation · polynomial compositions
OP-00231 Solution claimed
A uniform disk bound for wave-kernel Padé approximants
NA · backward error analysis · matrix functions · OpenProblemsInNLA · Padé approximants
OP-00232 Solution claimed
NP-hardness of unrestricted static output-feedback stabilization
OC · Hurwitz matrices · NP-hardness · OpenProblemsInNLA · static output feedback
OP-00233 Solution claimed
Uniqueness of positive definite solutions of two-letter word equations in order two
NA · nonlinear matrix equations · OpenProblemsInNLA · positive definite matrices · word equations
OP-00234 Solution claimed
Complete Crouzeix conjecture
FA · matrix polynomials · numerical ranges · OpenProblemsInNLA · spectral sets
OP-00235 Solution claimed
A dimension-independent polynomial norm bound from super-identical pseudospectra
NA · matrix polynomials · OpenProblemsInNLA · pseudospectra · singular values
OP-00236 Solution claimed
Preservation of real H-matrix structure by Newton square-root iterates
NA · H-matrices · matrix square roots · Newton iterations · OpenProblemsInNLA
OP-00237 Solution claimed
Clustered singular-value gaps in randomized block Krylov approximation
NA · Krylov subspace methods · low-rank approximations · OpenProblemsInNLA · singular value gaps
OP-00238 Solution claimed
Sharp joint rank and accuracy dependence for strong ℓₚ subspace coresets
NA · coresets · low-rank approximations · OpenProblemsInNLA · subspace approximation
OP-00239 Lean verified
Sensitivity-dependent row sampling for ℓₚ embeddings when p exceeds two
NA · OpenProblemsInNLA · row sampling · sensitivity sampling · subspace embeddings
OP-00240 Solution claimed
Concave-function transfer of spectral low-rank error
NA · low-rank approximations · matrix functions · Nyström approximations · OpenProblemsInNLA
OP-00241 Solution claimed
Concave-function transfer of Frobenius low-rank error
NA · low-rank approximations · matrix functions · Nyström approximations · OpenProblemsInNLA
OP-00242 Solution claimed
Constant-loss nuclear-error transfer without matrix ordering
NA · low-rank approximations · matrix functions · OpenProblemsInNLA · operator monotone functions
OP-00243 Solution claimed
Relative-error threshold for extremal Gaussian trace bounds
NA · Gamma distributions · OpenProblemsInNLA · tail bounds · trace estimation
OP-00244 Solution claimed
Absolute-error threshold for extremal Gaussian trace bounds
NA · Gamma distributions · OpenProblemsInNLA · tail bounds · trace estimation
OP-00245 Solution claimed
Critical-point count for corank-one approximation with a fixed zero
AG · determinantal varieties · Euclidean distance degrees · low-rank approximations · OpenProblemsInNLA
OP-00246 Solution claimed
Pure relative error for approximation by a linear matrix family
NA · matrix-vector queries · OpenProblemsInNLA · query complexity · structured matrices
OP-00247 Solution claimed
Nonadaptive queries for finite-family matrix approximation
NA · matrix-vector queries · nonadaptive algorithms · OpenProblemsInNLA · query complexity
OP-00248 Solution claimed
A sum-of-squares representation for the Toeplitz commutator form
FA · Böttcher–Wenzel inequality · OpenProblemsInNLA · sums of squares · Toeplitz matrices
OP-00249 Solution claimed
Schatten norm complement involving Lin's positive definite quantity
FA · matrix geometric means · norm inequalities · OpenProblemsInNLA · Schatten norms
OP-00250 Solution claimed
Ghabries's determinant comparison for arbitrary nonnegative base powers
FA · determinantal inequalities · OpenProblemsInNLA · positive definite matrices
OP-00251 Solution claimed
Sharp parameter dependence for structured Gaussian operator norms
PR · OpenProblemsInNLA · operator norms · random matrices
OP-00252 Lean verified
The delta conjecture for minimum symmetric rank
CO · inverse eigenvalue problems · maximum nullity · minimum rank · OpenProblemsInNLA
OP-00253 Solution claimed
A chromatic lower bound for positive-semidefinite nullity with SAP
CO · Colin de Verdière parameters · graph colorings · OpenProblemsInNLA · strong Arnold property
OP-00254 Solution claimed
Trace-norm-small perturbations preserve Hermitian spectral distributions
NA · eigenvalue distributions · matrix sequences · non-Hermitian perturbations · OpenProblemsInNLA
OP-00255 Solution claimed
Deciding accurate evaluability of real polynomials
NA · decision procedures · OpenProblemsInNLA · polynomial evaluation · rounding errors
OP-00256 Solution claimed
Recognizing the maximum finite number of solutions
NA · absolute value equations · OpenProblemsInNLA · piecewise linear systems
OP-00257 Solution claimed
Hardness of the spectral-norm condition number
NA · absolute value equations · condition numbers · interval matrices · OpenProblemsInNLA
OP-00258 Solution claimed
Sharp sampling complexity for Walsh restricted isometries
FA · compressed sensing · OpenProblemsInNLA · restricted isometry property · Walsh matrices
OP-00259 Solution claimed
Exact solution hulls for inverse M-matrix intervals
NA · interval matrices · inverse M-matrices · linear systems · OpenProblemsInNLA
OP-00260 Solution claimed
Complexity of globally optimal nonnegative rank-two approximation
NA · low-rank approximations · nonnegative matrix factorizations · OpenProblemsInNLA
OP-00261 Solution claimed
The maximum cp-rank in order six
NA · completely positive matrices · cp-rank · OpenProblemsInNLA
OP-00262 Solution claimed
Infinitesimal rigidity detects unique size-two factors in the presence of zeros
NA · infinitesimal rigidity · OpenProblemsInNLA · positive semidefinite factorizations · positive semidefinite rank
OP-00263 Partially resolved
The maximum permanent on a positive-semidefinite unitary orbit
FA · OpenProblemsInNLA · permanents · positive semidefinite matrices · unitary orbits
OP-00264 Partially resolved
Exact determinant ranges of general tridiagonal interval matrices
NA · determinants · interval matrices · OpenProblemsInNLA · tridiagonal matrices
OP-00265 Partially resolved
Exact solution hulls for tridiagonal interval systems
NA · interval matrices · linear systems · OpenProblemsInNLA · tridiagonal matrices
OP-00266 Open
Bourin's crossed-Heinz inequality
FA · norm inequalities · OpenProblemsInNLA · unitarily invariant norms
OP-00267 Open
Localization at every disorder strength in two dimensions
SP · AIM Open Applied Problems · Anderson localization · random Schrödinger operators
OP-00268 Open
Log-concavity of Gaussian convex-hull intersection probabilities
PR · AIM Open Applied Problems · Gaussian random points · log-concave sequences · Radon partitions
OP-00269 Open
Uniqueness of the stationary one-dependent four-coloring
PR · AIM Open Applied Problems · finitely dependent processes · proper colorings
OP-00270 Partially resolved
Pólya's eigenvalue inequalities
SP · AIM Open Applied Problems · Dirichlet eigenvalues · Neumann eigenvalues · Weyl's law
OP-00271 Solution claimed
Tail bounds for causal equivalence classes of uniform random DAGs
PR · AIM Open Applied Problems · directed acyclic graphs · Markov equivalence classes
OP-00272 Open
The spectral honeycomb conjecture
SP · AIM Open Applied Problems · Dirichlet eigenvalues · honeycomb conjecture · spectral minimal partitions
OP-00273 Open
The regular-polygon Steklov conjecture
SP · AIM Open Applied Problems · isoperimetric inequalities · polygons · Steklov eigenvalues
OP-00274 Solution claimed
Sharp least-singular-value bounds for independent random tensor columns
PR · AIM Open Applied Problems · random matrices · random tensors · singular values
OP-00275 Open
Bareket's conjecture for simply connected planar domains
SP · AIM Open Applied Problems · isoperimetric inequalities · Robin eigenvalues
OP-00276 Open
Polynomial-time Bernoulli group testing at the information threshold
ST · AIM Open Applied Problems · computational-statistical gaps · group testing
OP-00277 Open
Berry's random-wave conjecture as a local limit
SP · AIM Open Applied Problems · Laplace eigenfunctions · quantum chaos · random waves
OP-00278 Open
Support growth of the information-maximizing binomial prior
IT · AIM Open Applied Problems · capacity-achieving distributions · channel capacity
OP-00279 Open
A degree-two spectral gap for Brownian energy exchange
PR · AIM Open Applied Problems · Brownian energy process · interacting particle systems · spectral gaps
OP-00280 Open
The sharp ratio of the first two buckling eigenvalues
SP · AIM Open Applied Problems · buckling eigenvalues · clamped plates · eigenvalue ratios
OP-00281 Solution claimed
Pólya–Szegő conjecture for the first buckling load
SP · AIM Open Applied Problems · buckling eigenvalues · clamped plates · isoperimetric inequalities
OP-00282 Open
Hypergraph shuffles and the one-particle spectral gap
PR · AIM Open Applied Problems · hypergraphs · interchange process · spectral gaps
OP-00283 Open
Separation of measures by Cartan–Hadamard sliced distances
PR · AIM Open Applied Problems · Cartan–Hadamard manifolds · Radon transforms · sliced Wasserstein distances
OP-00284 Open
Polynomial-time DNF learning from uniform random examples
ST · AIM Open Applied Problems · Boolean functions · DNF formulas · PAC learning
OP-00285 Open
Dirichlet spectral determination of smooth strictly convex planar domains
SP · AIM Open Applied Problems · Dirichlet eigenvalues · inverse spectral problems · isospectral domains
OP-00286 Open
A fractal Weyl lower bound for obstacle resonances
SP · AIM Open Applied Problems · fractal Weyl laws · obstacle scattering · scattering resonances
OP-00287 Open
Orthogonal separation of independent Gaussian polynomial statistics
PR · AIM Open Applied Problems · characterization problems · Gaussian vectors · independence
OP-00288 Open
Ordinary posterior contraction for heavy-tailed neural-network priors
ST · AIM Open Applied Problems · Bayesian neural networks · heavy-tailed priors · posterior contraction
OP-00289 Open
Minimax entropy estimation beyond two derivatives
ST · AIM Open Applied Problems · differential entropy · functional estimation · minimax rates
OP-00290 Open
Ivrii's measure-zero conjecture for billiards
DS · AIM Open Applied Problems · billiards · periodic orbits · Weyl's law
OP-00291 Open
Classical hardness of learning parity with noise
IT · AIM Open Applied Problems · average-case complexity · learning parity with noise · random linear codes
OP-00292 Open
The three-dimensional Lieb–Thirring constant
SP · AIM Open Applied Problems · Lieb–Thirring inequalities · Schrödinger operators · sharp constants
OP-00293 Open
Linear-size sample compression for binary concept classes
CO · AIM Open Applied Problems · sample compression schemes · VC dimension
OP-00294 Open
Identifying a distribution from its Gaussian-channel MMSE curve
PR · AIM Open Applied Problems · Gaussian channels · minimum mean-square error
OP-00295 Open
The planar self-avoiding-walk displacement exponent
PR · AIM Open Applied Problems · critical exponents · self-avoiding walks
OP-00296 Open
Pólya–Szegő polygonal Faber–Krahn conjecture
SP · AIM Open Applied Problems · Dirichlet eigenvalues · Faber–Krahn inequality · polygons
OP-00297 Open
The polygonal Payne–Pólya–Weinberger ratio conjecture
SP · AIM Open Applied Problems · Dirichlet eigenvalues · eigenvalue ratios · polygons
OP-00298 Open
Oscillation of partition functions under very strong disorder
PR · AIM Open Applied Problems · directed polymers · random walks in random potentials
OP-00299 Open
Private PAC learning with polynomial VC and iterated-logarithm sample cost
ST · AIM Open Applied Problems · differential privacy · Littlestone dimension · PAC learning
OP-00300 Open
Perfect recovery threshold for unregularized quadratic-network training
PR · AIM Open Applied Problems · gradient flows · matrix sensing · quadratic neural networks
OP-00301 Open
Quantum unique ergodicity in negative curvature
SP · AIM Open Applied Problems · Laplace eigenfunctions · quantum ergodicity · semiclassical measures
OP-00302 Open
Classifying Gaussian models with rational maximum-likelihood estimators
ST · AIM Open Applied Problems · Gaussian models · homaloidal polynomials · maximum likelihood estimators
OP-00303 Open
Rayleigh's clamped-plate conjecture in higher dimensions
SP · AIM Open Applied Problems · biharmonic eigenvalues · clamped plates · isoperimetric inequalities
OP-00304 Open
Mixing time of the reflected Burnside sampler for integer partitions
PR · AIM Open Applied Problems · Burnside process · integer partitions · mixing times
OP-00305 Solution claimed
Strong freeness for one random interaction on overlapping tensor legs
PR · AIM Open Applied Problems · free probability · strong convergence · tensor GUE matrices
OP-00306 Open
The Robin eigenvalue ratio at fixed volume
SP · AIM Open Applied Problems · eigenvalue ratios · isoperimetric inequalities · Robin eigenvalues
OP-00307 Open
The sharp planar Pleijel constant
SP · AIM Open Applied Problems · Dirichlet eigenfunctions · nodal domains · Pleijel's theorem
OP-00308 Open
The sharp support–concentration bound for subset sums
PR · AIM Open Applied Problems · anticoncentration · Rényi entropies · subset sums
OP-00309 Open
Does the disk minimize the third Dirichlet eigenvalue?
SP · AIM Open Applied Problems · Dirichlet eigenvalues · spectral shape optimization
OP-00310 Open
Monotonicity of draw probabilities under random vertex deletion
PR · AIM Open Applied Problems · combinatorial games · site percolation
OP-00311 Open
Simes error control for two-sided Gaussian tests
ST · AIM Open Applied Problems · multiple testing · Simes inequality · two-sided tests
OP-00312 Open
Unimodality of Radon partitions for uniform convex samples
PR · AIM Open Applied Problems · Radon partitions · Sylvester's four-point problem · unimodal sequences
OP-00313 Open
Low-degree representations determining a unitary shuffle's gap
PR · AIM Open Applied Problems · random walks on groups · spectral gaps · unitary groups
OP-00314 Open
Polynomial-time proper learning of univariate Gaussian mixtures
ST · AIM Open Applied Problems · density estimation · Gaussian mixtures · proper learning
OP-00315 Open
Minimax estimation of topic distributions with weak sparsity
ST · AIM Open Applied Problems · minimax rates · sparse estimation · topic models
OP-00316 Solution claimed
The sharp Beurling–Ahlfors bound for planar elliptic systems
CA · AIM Open Applied Problems · Beurling–Ahlfors transform · quasiconformal mappings · singular integrals
OP-00317 Open
Excess Floquet multiplicity for complex periodic Schrödinger equations
SP · AIM Open Applied Problems · Hill operators · non-self-adjoint operators · periodic eigenvalues
OP-00318 Solution claimed
Uniqueness of the critical catenoid
DG · AIM Open Applied Problems · critical catenoid · free boundary minimal surfaces · Steklov eigenvalues
OP-00319 Solution claimed
The modern integer 3SUM conjecture
CO · 3SUM · AIM Open Applied Problems · fine-grained complexity · word RAM algorithms
OP-00320 Solution claimed
A real nearest matrix with spectrum in the closed left half-plane
NA · AIM Open Applied Problems · Hurwitz stable matrices · matrix nearness problems
OP-00321 Solution claimed
A universal central limit law for quantum-graph nodal surplus
SP · AIM Open Applied Problems · central limit theorems · nodal counts · quantum graphs
OP-00322 Solution claimed
Quadratic-scale bit complexity for well-conditioned sparse systems
NA · AIM Open Applied Problems · bit complexity · sparse linear systems
OP-00323 Open
A constant bound for fixed-order prefix discrepancy
CO · AIM Open Applied Problems · Komlós conjecture · prefix discrepancy · vector balancing
OP-00324 Open
Aaronson–Ambainis influential-variable conjecture
CO · AIM Open Applied Problems · Boolean functions · influences · quantum query complexity
OP-00325 Solution claimed
Accurate selected bidiagonal singular vectors in O(kn) work
NA · AIM Open Applied Problems · bidiagonal matrices · floating-point algorithms · singular value decompositions
OP-00326 Open
Diffusive mean-square displacement at fixed disorder
MP · AIM Open Applied Problems · Anderson model · quantum diffusion · random Schrödinger operators
OP-00327 Open
Arveson–Douglas essential normality for homogeneous ideals
FA · AIM Open Applied Problems · Drury–Arveson space · essential normality · Schatten classes
OP-00328 Open
Unbounded chromatic number of associahedron graphs
CO · AIM Open Applied Problems · associahedra · flip graphs · graph colorings
OP-00329 Open
Convexity of atomic ground-state energy in electron number
SP · AIM Open Applied Problems · ionization energies · many-electron atoms
OP-00330 Open
Classifying balanced elementary symmetric Boolean functions
CO · AIM Open Applied Problems · elementary symmetric polynomials · symmetric Boolean functions
OP-00331 Open
Baur’s high-field disk conjecture for all higher eigenvalues
SP · AIM Open Applied Problems · Dirichlet eigenvalues · isoperimetric inequalities · magnetic Laplacians
OP-00332 Open
The symmetry point of a unimodular lattice's secrecy function
NT · AIM Open Applied Problems · theta series · unimodular lattices · wiretap codes
OP-00333 Open
Bos's cubic and quartic simplex interpolation nodes
NA · AIM Open Applied Problems · Fekete points · Lagrange interpolation · optimal designs
OP-00334 Open
A sharp universal inequality for clamped-plate eigenvalues
SP · AIM Open Applied Problems · biharmonic operators · clamped plates · universal inequalities
OP-00335 Open
Irreducibility of complex Fermi varieties
SP · AIM Open Applied Problems · embedded eigenvalues · Fermi varieties · periodic Schrödinger operators
OP-00336 Open
Boundary contact of the second nodal set in convex domains
SP · AIM Open Applied Problems · convex domains · Dirichlet eigenfunctions · nodal sets
OP-00337 Open
Costas arrays at every order
CO · AIM Open Applied Problems · Costas arrays · permutation arrays
OP-00338 Open
Classifying Costas polynomials over extension fields
NT · AIM Open Applied Problems · Costas polynomials · finite fields · permutation polynomials
OP-00339 Open
Exact quantum capacity of the qubit depolarizing channel
IT · AIM Open Applied Problems · coherent information · depolarizing channels · quantum channel capacities
OP-00340 Open
Deterministic identity testing for arithmetic circuits
AC · AIM Open Applied Problems · arithmetic circuits · derandomization · polynomial identity testing
OP-00341 Open
Concentration of nuclear charge minimizes the Dirac gap level
SP · AIM Open Applied Problems · Coulomb potentials · Dirac operators · eigenvalue optimization
OP-00342 Open
The three-quarter conjecture for binary fix-free codes
CO · AIM Open Applied Problems · fix-free codes · Kraft inequality · variable-length codes
OP-00343 Solution claimed
Arbitrarily large Steklov frequency with a prescribed embedded boundary
SP · AIM Open Applied Problems · prescribed boundary · Steklov eigenvalues · submanifolds
OP-00344 Open
Linear inverse bounds for four-diamond scattering
NA · AIM Open Applied Problems · boundary integral equations · Helmholtz equation · trapping obstacles
OP-00345 Partially resolved
The Fourier entropy–influence conjecture
CO · AIM Open Applied Problems · Boolean functions · Fourier coefficients · influences
OP-00346 Open
The first Steklov eigenvalue of a free-boundary minimal hypersurface
DG · AIM Open Applied Problems · free boundary minimal surfaces · Steklov eigenvalues
OP-00347 Open
Full-order resonance growth for every nonzero real compact potential
SP · AIM Open Applied Problems · scattering resonances · Schrödinger operators
OP-00348 Open
Hexagonal optimality for Gaussian time-frequency sampling
FA · AIM Open Applied Problems · frame bounds · Gabor frames · hexagonal lattices
OP-00349 Open
Deterministic parallel perfect matching in general graphs
CO · AIM Open Applied Problems · derandomization · parallel algorithms · perfect matchings
OP-00350 Open
Perfect Lee codes beyond dimension two
CO · AIM Open Applied Problems · Lee metric · perfect codes · tilings
OP-00351 Open
Decomposing complete graphs into squares of Hamilton cycles
CO · AIM Open Applied Problems · combinatorial designs · graph decompositions · Hamilton cycles
OP-00352 Open
Excluding three correlation levels in quadratic field towers
NT · AIM Open Applied Problems · finite fields · m-sequences · Weil sums
OP-00353 Open
A zero in the nontrivial spectrum of a power permutation
NT · AIM Open Applied Problems · m-sequences · power permutations · Weil sums
OP-00354 Solution claimed
Sharp barrier-parameter growth for hyperbolic balls
OC · AIM Open Applied Problems · Hadamard manifolds · interior-point methods · self-concordant barriers
OP-00355 Open
Completeness of modes for slowly growing imaginary Schrödinger potentials
SP · AIM Open Applied Problems · completeness of eigenfunctions · non-self-adjoint operators · Schrödinger operators
OP-00356 Open
Jakobson–Naud’s essential spectral-gap conjecture
SP · AIM Open Applied Problems · hyperbolic surfaces · scattering resonances · spectral gaps
OP-00357 Open
The log-rank conjecture for deterministic communication
CO · AIM Open Applied Problems · Boolean matrices · communication complexity · matrix rank
OP-00358 Partially resolved
Low-degree convergence of relaxed minimal-deformation surface elements
NA · AIM Open Applied Problems · evolving surface finite elements · surface evolution · tangential motions
OP-00359 Open
Nonempty spectrum for a magnetic complex Airy operator at every field strength
SP · AIM Open Applied Problems · magnetic Schrödinger operators · non-self-adjoint operators · superconductivity
OP-00360 Open
The disk maximizes the first magnetic Neumann eigenvalue
SP · AIM Open Applied Problems · isoperimetric inequalities · magnetic Laplacians · Neumann eigenvalues
OP-00361 Open
Strict angle monotonicity of magnetic wedge ground energy
SP · AIM Open Applied Problems · corner domains · magnetic Laplacians
OP-00362 Solution claimed
A universal bound on excess molecular charge
SP · AIM Open Applied Problems · Coulomb systems · negative ions
OP-00363 Open
Infinitely many obstacle resonances in a fixed strip under trapping
AP · AIM Open Applied Problems · billiards · obstacle scattering · scattering resonances
OP-00364 Open
A sharp Galerkin projection bound on nonobtuse triangles
NA · AIM Open Applied Problems · Galerkin projections · hybrid high-order methods · nonobtuse triangles
OP-00365 Open
Existence of NPT bound entanglement
MP · AIM Open Applied Problems · bound entanglement · entanglement distillation · Werner states
OP-00366 Open
Is the optimal magnetic rectangle always a square?
SP · AIM Open Applied Problems · Dirichlet eigenvalues · magnetic Laplacians
OP-00367 Solution claimed
Smallest orders for periodic multidimensional Costas arrays
CO · AIM Open Applied Problems · Costas arrays · permutation arrays
OP-00368 Open
Absolute continuity for smooth periodic scalar elliptic operators
SP · AIM Open Applied Problems · periodic elliptic operators · spectral measures
OP-00369 Open
Removable cycles in cycle permutation graphs
CO · AIM Open Applied Problems · cycle permutation graphs · removable cycles · snarks
OP-00370 Open
Permutation snarks without five-cycles
CO · AIM Open Applied Problems · cycle permutation graphs · edge colourings · snarks
OP-00371 Open
Permutation snarks with order congruent to six modulo eight
CO · AIM Open Applied Problems · cubic graphs · edge colorings · snarks
OP-00372 Open
The sharp asymptotic facial length in girth-saturated plane graphs
CO · AIM Open Applied Problems · girth · graph saturation · plane graphs
OP-00373 Open
Polynomial-size nonobtuse tetrahedral meshes
MG · AIM Open Applied Problems · mesh generation · nonobtuse tetrahedra · triangulations
OP-00374 Open
Faber–Krahn inequality for graphene quantum dots
SP · AIM Open Applied Problems · Dirac operators · Faber–Krahn inequalities
OP-00375 Open
Are the standard quantum entropy inequalities complete?
IT · AIM Open Applied Problems · entropy cones · entropy inequalities · von Neumann entropy
OP-00376 Open
The exact real Grothendieck constant
FA · AIM Open Applied Problems · Grothendieck inequality · semidefinite relaxations · sharp constants
OP-00377 Open
Reed's bound for the chromatic number
CO · AIM Open Applied Problems · chromatic number · graph colorings
OP-00378 Open
Can bound entanglement produce a device-independent secret key?
IT · AIM Open Applied Problems · bound entanglement · quantum information · quantum key distribution
OP-00379 Open
Subpolynomial compact-set peaks of Hecke–Maass waves
NT · AIM Open Applied Problems · arithmetic quantum chaos · Maass forms · sup norms
OP-00380 Open
Global uniqueness of fine-mesh semilinear Galerkin solutions
NA · AIM Open Applied Problems · control problems · finite element methods · semilinear elliptic equations
OP-00381 Open
Simon’s multidimensional weighted square-integrability conjecture
SP · absolutely continuous spectrum · AIM Open Applied Problems · decaying potentials · Schrödinger operators
OP-00382 Open
Global convergence of the simple CRDT conformal-mapping iteration
NA · AIM Open Applied Problems · cross-ratios · numerical conformal mapping · Schwarz–Christoffel maps
OP-00383 Open
Anderson localization for the cosine skew-shift model at every coupling
SP · AIM Open Applied Problems · Anderson localization · discrete Schrödinger operators · skew-shifts
OP-00384 Open
Sharp permutation bound for triangular parts of correlation matrices
NA · AIM Open Applied Problems · correlation matrices · SOR methods · triangular truncation
OP-00385 Open
The Weinstock inequality for convex domains in a sphere
SP · AIM Open Applied Problems · convex domains · isoperimetric inequalities · Steklov eigenvalues
OP-00386 Solution claimed
Reality of the spectrum for a spherical strip with PT-symmetric boundary conditions
SP · AIM Open Applied Problems · non-self-adjoint operators · PT-symmetric operators · Robin boundary conditions
OP-00387 Open
Dynamic optimality of splay trees
CO · AIM Open Applied Problems · binary search trees · dynamic optimality · splay trees
OP-00388 Open
Optimal stable manifold widths of Besov balls
NA · AIM Open Applied Problems · Besov spaces · nonlinear approximation · nonlinear widths
OP-00389 Open
Optimal star-discrepancy lower bound for infinite sequences
NT · AIM Open Applied Problems · discrepancy · low-discrepancy sequences · quasi-Monte Carlo methods
OP-00390 Solution claimed
Unbounded first Steklov multiplicity with fixed boundary count
SP · AIM Open Applied Problems · eigenvalue multiplicities · Riemannian surfaces · Steklov eigenvalues
OP-00391 Open
Divisible point sets as unions of parallel lines
CO · AIM Open Applied Problems · direction problems · divisible codes · finite geometry
OP-00392 Open
A strongly polynomial pivot rule for the simplex method
OC · AIM Open Applied Problems · linear programming · pivot rules · simplex method
OP-00393 Open
Sunada’s no-gap conjecture for abelian covers
SP · abelian coverings · AIM Open Applied Problems · hyperbolic surfaces · spectral gaps
OP-00394 Solution claimed
A linear genus–girth bound for facial cycles
CO · AIM Open Applied Problems · facial cycles · girth · graphs on surfaces
OP-00395 Solution claimed
An optimal Weyl remainder for interior transmission eigenvalues
SP · AIM Open Applied Problems · interior transmission eigenvalues · non-self-adjoint operators · Weyl's law
OP-00396 Open
Maximum treewidth at a prescribed edge count
CO · AIM Open Applied Problems · extremal problems · tree decompositions · treewidth
OP-00397 Partially resolved
The factor-two relation between triangle deletion and packing
CO · AIM Open Applied Problems · triangle covers · triangle packings · Tuza's conjecture
OP-00398 Partially resolved
Uniformly effective algebraic multigrid for diagonally dominant systems
NA · AIM Open Applied Problems · algebraic multigrid · diagonally dominant matrices · preconditioners
OP-00399 Open
The sharp vector Riesz inequality for multidimensional potential fields
CA · AIM Open Applied Problems · Riesz transforms · sharp constants · singular integrals
OP-00400 Solution claimed
Optimal spectral signings of regular graphs
CO · AIM Open Applied Problems · graph lifts · Ramanujan graphs · signed graphs
OP-00401 Solution claimed
Non-explosion of Brownian Fleming–Viot systems in arbitrary domains
PR · AIM Open Applied Problems · Fleming–Viot particle systems · killed Brownian motion
OP-00402 Solution claimed
Additivity of entanglement of purification
MP · additivity · AIM Open Applied Problems · entanglement of purification · von Neumann entropy
OP-00403 Solution claimed
Does supercritical percolation preserve transience?
PR · AIM Open Applied Problems · Cayley graphs · percolation · random walks
OP-00404 Solution claimed
The sharp matroid secretary conjecture
OC · AIM Open Applied Problems · matroids · online algorithms · secretary problems
OP-00405 Open
The density conjecture for activated random walk on the square lattice
PR · activated random walk · AIM Open Applied Problems · interacting particle systems · self-organized criticality
OP-00406 Open
The factor-two integrality gap for asymmetric metric routing
OC · AIM Open Applied Problems · integrality gaps · linear programming relaxations · traveling salesman problem
OP-00407 Open
Consensus in the one-dimensional Axelrod model above the feature threshold
PR · AIM Open Applied Problems · Axelrod model · clustering · interacting particle systems
OP-00408 Open
Poisson nearest-neighbor spacings on almost every flat torus
NT · AIM Open Applied Problems · binary quadratic forms · flat tori · level spacings
OP-00409 Open
The exact asymptotic match fraction for independent binary sequences
PR · AIM Open Applied Problems · longest common subsequences · random sequences
OP-00410 Open
Is the variance of fair binary sequence alignment linear?
PR · AIM Open Applied Problems · longest common subsequences · sequence alignment · variance bounds
OP-00411 Open
Does a bound bipolaron ever break rotational symmetry?
MP · AIM Open Applied Problems · polarons · symmetry breaking
OP-00412 Open
Bourgain–Spencer accuracy for random elliptic media at finite contrast
AP · AIM Open Applied Problems · higher-order homogenized equations · stochastic homogenization
OP-00413 Solution claimed
Selection of the carbon-monoxide poisoning phase
PR · absorbing states · AIM Open Applied Problems · catalytic surface reactions · interacting particle systems
OP-00414 Open
Competitive exclusion in a chemostat with unequal removal rates
DS · AIM Open Applied Problems · chemostats · competitive exclusion · Lyapunov functions
OP-00415 Open
Rapid sampling of proper colorings at the ergodicity threshold
PR · AIM Open Applied Problems · Glauber dynamics · mixing times · proper colorings
OP-00416 Open
Competitive exclusion with unequal death rates
PR · AIM Open Applied Problems · competitive exclusion · multitype contact process
OP-00417 Open
Subunit-moment eigenvalue bounds for complex Schrödinger potentials
SP · AIM Open Applied Problems · complex potentials · Lieb–Thirring inequalities · non-self-adjoint operators
OP-00418 Open
Weak survival of the contact process on nonamenable Cayley graphs
PR · AIM Open Applied Problems · Cayley graphs · contact process · nonamenable groups
OP-00419 Open
Polynomial equilibration at the four-state planar Potts critical point
PR · AIM Open Applied Problems · Glauber dynamics · mixing times · Potts model
OP-00420 Solution claimed
Global regularity for critical SQG with state-dependent noise
PR · AIM Open Applied Problems · global regularity · multiplicative noise · surface quasi-geostrophic equations
OP-00421 Solution claimed
Does subcritical heat flow always decay faster?
AP · AIM Open Applied Problems · criticality theory · heat kernels · Schrödinger operators
OP-00422 Open
Coexistence for every positive cyclic invasion rate
PR · AIM Open Applied Problems · coexistence · cyclic competition · interacting particle systems
OP-00423 Open
Constant-gap NP-hardness of densest k-subgraph
CO · AIM Open Applied Problems · densest k-subgraph · hardness of approximation
OP-00424 Solution claimed
A continuous strictly decreasing moment spectrum for Gaussian polymers
PR · AIM Open Applied Problems · directed polymers · disordered systems · martingales
OP-00425 Open
Classical attenuation versus uniform semiclassical local decay
AP · AIM Open Applied Problems · dissipative Schrödinger operators · local decay · semiclassical analysis
OP-00426 Open
A deterministic nontrivial growth exponent for planar DLA
PR · AIM Open Applied Problems · diffusion-limited aggregation · harmonic measure · random growth models
OP-00427 Open
Positive-temperature order in the three-dimensional Edwards–Anderson spin glass
PR · AIM Open Applied Problems · Edwards–Anderson model · replica overlaps · spin glasses
OP-00428 Open
Complete EFX allocation of indivisible goods with additive values
CO · AIM Open Applied Problems · envy-free allocations · fair division
OP-00429 Open
Does entanglement-assisted capacity equal the Lovász bound?
CO · AIM Open Applied Problems · entanglement-assisted communication · Lovász number · zero-error capacities
OP-00430 Open
Gaussian fluctuations of the optimal Euclidean traveling-salesman tour
PR · AIM Open Applied Problems · central limit theorems · geometric probability · traveling salesman problem
OP-00431 Open
Does exclusion equilibrate as fast as independent particles?
PR · AIM Open Applied Problems · exclusion processes · interacting particle systems · mixing times
OP-00432 Solution claimed
Accuracy of parsimony reconstruction under a molecular clock
PR · AIM Open Applied Problems · ancestral state reconstruction · maximum parsimony · phylogenetic trees
OP-00433 Open
The two-thirds passage-time variance exponent
PR · AIM Open Applied Problems · first-passage percolation · fluctuation exponents · KPZ universality
OP-00434 Open
Monotonicity of transport speed on Galton–Watson trees
PR · AIM Open Applied Problems · biased random walks · Galton–Watson trees
OP-00435 Open
Tracy–Widom fluctuations for a Gaussian lattice polymer at fixed temperature
PR · AIM Open Applied Problems · directed polymers · KPZ universality · Tracy–Widom distribution
OP-00436 Open
Balanced Gaussian simplex noise stability for four or more classes
PR · AIM Open Applied Problems · Gaussian partitions · noise stability
OP-00437 Open
A constant approximation for general max-min fair allocation
OC · AIM Open Applied Problems · approximation algorithms · max-min fair allocation
OP-00438 Open
The GNRS conjecture for minor-free network flow
CO · AIM Open Applied Problems · graph minors · metric embeddings · multicommodity flows
OP-00439 Open
A phase transition for continuum hard disks
PR · AIM Open Applied Problems · Gibbs point processes · hard disks · phase transitions
OP-00440 Open
A periodic high-density limit for bounded-confidence opinion clusters
PR · AIM Open Applied Problems · Hegselmann–Krause model · opinion dynamics · Poisson point processes
OP-00441 Open
Antiferromagnetic order in the half-filled square-lattice Hubbard model
MP · AIM Open Applied Problems · antiferromagnetism · Hubbard models · long-range order
OP-00442 Open
Global L2 scattering for the planar hyperbolic cubic Schrödinger equation
AP · AIM Open Applied Problems · dispersive equations · nonlinear Schrödinger equations · scattering
OP-00443 Open
A resonance gap for arbitrary uniformly hyperbolic trapping in three dimensions
SP · AIM Open Applied Problems · hyperbolic trapped sets · scattering resonances · semiclassical analysis
OP-00444 Open
Does stronger ferromagnetic coupling always slow Ising relaxation?
PR · AIM Open Applied Problems · Glauber dynamics · Ising model · spectral gaps
OP-00445 Open
Polynomial mixing of planar Ising dynamics with plus boundary
PR · AIM Open Applied Problems · Glauber dynamics · Ising model · mixing times
OP-00446 Open
A constant comparison between systematic and random Ising updates
PR · AIM Open Applied Problems · Glauber dynamics · Ising model · mixing times
OP-00447 Open
A roughening transition in the three-dimensional Ising model
PR · AIM Open Applied Problems · Gibbs measures · interfaces · Ising model
OP-00448 Open
The bosonic Laughlin contact-interaction gap
MP · AIM Open Applied Problems · Laughlin states · rotating Bose gases · spectral gaps
OP-00449 Open
Uniqueness of a boson star at every subcritical mass
AP · AIM Open Applied Problems · boson stars · ground states · pseudo-relativistic Hartree equations
OP-00450 Open
Liouville invariance under changing local moves on a Cayley network
PR · AIM Open Applied Problems · Liouville property · Poisson boundaries · random walks on groups
OP-00451 Open
List edge-colouring with no extra colours
CO · AIM Open Applied Problems · edge colourings · list colourings · multigraphs
OP-00452 Open
Does every strict initial majority win zero-temperature Ising dynamics?
PR · AIM Open Applied Problems · coarsening · Glauber dynamics · Ising models
OP-00453 Open
The four-thirds integrality gap for metric routing
CO · AIM Open Applied Problems · integrality gaps · linear programming relaxations · traveling salesman problem
OP-00454 Open
Does local stability imply global attraction for Nicholson’s blowflies equation?
DS · AIM Open Applied Problems · delay differential equations · global attractivity · Nicholson's blowflies equation
OP-00455 Open
Optimal asymptotic competitiveness for online bin packing
OC · AIM Open Applied Problems · bin packing · competitive ratios · online algorithms
OP-00456 Open
The optimal Lieb–Oxford constant
MP · AIM Open Applied Problems · density functional theory · indirect Coulomb energies · Lieb–Oxford inequality
OP-00457 Solution claimed
Strong disorder versus a shifted pinning threshold
PR · AIM Open Applied Problems · disordered systems · pinning models · renewal processes
OP-00458 Open
Localization of light rays in the planar random mirror model
PR · AIM Open Applied Problems · Lorentz mirror model · random environments
OP-00459 Open
Existence of a planar sandpile avalanche-size exponent
PR · Abelian sandpiles · AIM Open Applied Problems · critical exponents · self-organized criticality
OP-00460 Open
Uniqueness of the planar spin-glass ground-state pair
PR · AIM Open Applied Problems · Edwards–Anderson model · ground states · spin glasses
OP-00461 Open
The sharp savings from junctions in planar connection networks
MG · AIM Open Applied Problems · minimum spanning trees · Steiner minimal trees
OP-00462 Open
Two stationary phases in a positive-rate nonlinear voter perturbation
PR · AIM Open Applied Problems · interacting particle systems · nonlinear voter models
OP-00463 Open
Can bounded positive time-dependent potentials trap a Schrödinger wave?
MP · AIM Open Applied Problems · bound states · Schrödinger equations · time-dependent potentials
OP-00464 Open
Global quadratic reaction–diffusion systems with general transport noise
PR · AIM Open Applied Problems · reaction–diffusion systems · stochastic PDEs · transport noise
OP-00465 Open
The quantum PCP conjecture for local Hamiltonians
MP · AIM Open Applied Problems · local Hamiltonians · probabilistically checkable proofs · QMA
OP-00466 Open
Positive recurrence of every weakly reversible stochastic reaction network
PR · AIM Open Applied Problems · chemical reaction networks · continuous-time Markov chains · positive recurrence
OP-00467 Open
Boundary-flux commutators for rough conductors
AP · AIM Open Applied Problems · commutator estimates · Dirichlet-to-Neumann operators · rough coefficients
OP-00468 Open
The sharp decay rate for waves damped on a disk
AP · AIM Open Applied Problems · damped wave equations · energy decay · resolvent estimates
OP-00469 Open
Hölder continuity for parabolic SPDEs with merely bounded transport noise
PR · AIM Open Applied Problems · De Giorgi–Nash–Moser estimates · stochastic PDEs · transport noise
OP-00470 Open
Equal-weight decomposition of quantum channels with bounded Kraus rank
MP · AIM Open Applied Problems · convex decompositions · Kraus rank · quantum channels
OP-00471 Open
Bolthausen–Sznitman ancestry for a fixed-size selected population
PR · AIM Open Applied Problems · branching Brownian motion · coalescents · genealogies
OP-00472 Open
GOE level spacings in a desymmetrized Sinai billiard
SP · AIM Open Applied Problems · level spacings · quantum chaos · random matrices
OP-00473 Solution claimed
A deterministic Hölder exponent for smooth-transport parabolic SPDEs
PR · AIM Open Applied Problems · De Giorgi–Nash–Moser estimates · stochastic PDEs · transport noise
OP-00474 Open
Spatial coexistence despite extinction in the mean-field game
PR · AIM Open Applied Problems · coexistence · evolutionary games · interacting particle systems
OP-00475 Open
Néel order in the square-lattice spin-one-half antiferromagnet
MP · AIM Open Applied Problems · long-range order · quantum Heisenberg antiferromagnets
OP-00476 Open
Pathwise uniqueness at the three-quarter Hölder threshold
PR · AIM Open Applied Problems · pathwise uniqueness · space-time white noise · stochastic heat equations
OP-00477 Open
A bounded critical norm continuation criterion for stochastic Navier–Stokes
PR · AIM Open Applied Problems · blow-up criteria · stochastic Navier–Stokes equations · transport noise
OP-00478 Solution claimed
Transport-noise Navier–Stokes at critical smoothness minus one half
PR · AIM Open Applied Problems · critical spaces · Navier–Stokes equations · transport noise
OP-00479 Solution claimed
Local no-slip Navier–Stokes theory under non-small transport noise
PR · AIM Open Applied Problems · no-slip boundary conditions · stochastic Navier–Stokes equations · transport noise
OP-00480 Open
A spectral gap for almost every pair of quantum gates
GR · AIM Open Applied Problems · random walks on compact groups · spectral gaps
OP-00481 Open
Optimal symmetric rendezvous among discrete locations
OC · AIM Open Applied Problems · rendezvous search · search games
OP-00482 Open
Connectivity of the three-dimensional minimal spanning forest
PR · AIM Open Applied Problems · invasion percolation · minimal spanning forests
OP-00483 Open
Coexistence in a three-strain colicin model
PR · AIM Open Applied Problems · allelopathy · coexistence · interacting particle systems
OP-00484 Open
Abrupt equilibration on every family of transitive expanders
PR · AIM Open Applied Problems · cutoff phenomenon · expander graphs · vertex-transitive graphs
OP-00485 Open
A diameter bound for diffusion to uniform equilibrium
PR · AIM Open Applied Problems · mixing times · random walks on graphs · vertex-transitive graphs
OP-00486 Open
Exclusion of coexistence for unequal Richardson growth rates
PR · AIM Open Applied Problems · competing growth · first-passage percolation · Richardson model
OP-00487 Open
Polynomial-factor hardness of scheduling unit jobs on prescribed machines
OC · AIM Open Applied Problems · hardness of approximation · precedence constraints · scheduling
OP-00488 Open
Beat factor two for scheduling on unrelated machines
OC · AIM Open Applied Problems · approximation algorithms · scheduling · unrelated parallel machines
OP-00489 Open
The logarithmic correction to dilute Bose-gas energy
MP · AIM Open Applied Problems · dilute Bose gases · ground-state energies
OP-00490 Solution claimed
Continuity of states driven by bounded admissible inputs
OC · admissible control operators · AIM Open Applied Problems · input-to-state stability · operator semigroups
OP-00491 Solution claimed
Nonbranching of analytic equiregular sub-Riemannian geodesics
DG · AIM Open Applied Problems · branching geodesics · sub-Riemannian geodesics
OP-00492 Solution claimed
The Li–Li multiple-unicast conjecture
IT · AIM Open Applied Problems · multicommodity flows · network coding
OP-00493 Solution claimed
Pansu's isoperimetric conjecture in the Heisenberg group
DG · AIM Open Applied Problems · Heisenberg group · isoperimetric inequalities · sub-Riemannian geometry
OP-00494 Open
A periodic nonsingular billiard trajectory in every triangle
DS · AIM Open Applied Problems · periodic orbits · polygonal billiards · triangles
OP-00495 Solution claimed
Decidability of local asymptotic stability for polynomial ODEs
DS · AIM Open Applied Problems · asymptotic stability · decidability · polynomial vector fields
OP-00496 Solution claimed
Sharp vanishing-viscosity control time for downstream transport
OC · AIM Open Applied Problems · null controllability · transport-diffusion equations · vanishing viscosity limits
OP-00497 Solution claimed
Sard conjecture for smooth bracket-generating distributions
DG · abnormal curves · AIM Open Applied Problems · endpoint maps · sub-Riemannian geometry
OP-00498 Open
Almost-everywhere global existence for Newtonian gravitation
DS · AIM Open Applied Problems · celestial mechanics · n-body problems · noncollision singularities
OP-00499 Open
Continuous selection of small-time null controls for analytic systems
OC · AIM Open Applied Problems · control-affine systems · feedback stabilization · small-time local controllability
OP-00500 Open
The sharp Belgian chocolate stabilization threshold
OC · AIM Open Applied Problems · Belgian chocolate problem · simultaneous stabilization · stable polynomials
OP-00501 Open
The optimal asymptotic rate of binary error-correcting codes
IT · AIM Open Applied Problems · error-correcting codes · Gilbert–Varshamov bound · linear programming bounds
OP-00502 Open
Exact capacity of the binary deletion channel
IT · AIM Open Applied Problems · channel capacity · deletion channels · synchronization errors
OP-00503 Open
Symmetric capacity of the binary multiplying two-way channel
IT · AIM Open Applied Problems · channel capacity · interactive communication · two-way channels
OP-00504 Open
Capacity of the binary skew-symmetric broadcast channel
IT · AIM Open Applied Problems · broadcast channels · channel capacity · Marton's inner bound
OP-00505 Open
A complete boundary-control criterion for coupled heat systems in higher dimensions
OC · AIM Open Applied Problems · boundary controllability · coupled parabolic systems
OP-00506 Open
Continuous velocity of every sub-Riemannian length minimizer
DG · abnormal minimizers · AIM Open Applied Problems · sub-Riemannian geodesics
OP-00507 Open
The Černý synchronizing-automaton conjecture
CO · AIM Open Applied Problems · Černý conjecture · reset words · synchronizing automata
OP-00508 Open
An SRB measure for the classical Hénon parameters
DS · AIM Open Applied Problems · Hénon maps · SRB measures · strange attractors
OP-00509 Open
A sharp surface-area bound for the convex hull of a closed curve
MG · AIM Open Applied Problems · convex hulls · isoperimetric inequalities · space curves
OP-00510 Open
Maximum convex-hull volume for a closed curve of fixed length
MG · AIM Open Applied Problems · convex hulls · isoperimetric problems · space curves
OP-00511 Open
Minimum volume of a three-dimensional body of constant width
MG · AIM Open Applied Problems · Blaschke–Lebesgue problem · bodies of constant width · Meissner bodies
OP-00512 Open
A strictly convex function on every simple manifold
DG · AIM Open Applied Problems · boundary rigidity · simple manifolds · strictly convex functions
OP-00513 Open
Exactly n or infinitely many periodic orbits on a convex energy surface
SG · AIM Open Applied Problems · closed characteristics · convex hypersurfaces · Reeb flows
OP-00514 Open
The least-area convex cover of every unit-length planar curve
MG · AIM Open Applied Problems · Moser's worm problem · universal covers
OP-00515 Open
Asymptotic density of reflected wavefronts in a disk
DS · AIM Open Applied Problems · billiards · wave fronts
OP-00516 Open
An overlap-free edge unfolding for every convex polyhedron
MG · AIM Open Applied Problems · convex polyhedra · edge unfoldings · nets
OP-00517 Open
Injectivity with attenuation of finite angular degree
DG · AIM Open Applied Problems · attenuated ray transforms · geometric inverse problems · simple surfaces
OP-00518 Open
Irrational ellipticity when a convex energy surface has finitely many orbits
DS · AIM Open Applied Problems · closed characteristics · convex hypersurfaces · linear stability
OP-00519 Solution claimed
Finite-jet determination of small-time local controllability
OC · AIM Open Applied Problems · control-affine systems · nonlinear control · small-time local controllability
OP-00520 Partially resolved
Finiteness of planar central configurations for fixed masses
DS · AIM Open Applied Problems · central configurations · n-body problems · relative equilibria
OP-00521 Open
Recover an arbitrary sound speed from one incident direction
AP · AIM Open Applied Problems · fixed angle scattering · inverse scattering · sound speeds
OP-00522 Open
Capacity of the two-receiver Gaussian broadcast channel with feedback
IT · AIM Open Applied Problems · broadcast channels · channel capacity · Gaussian channels
OP-00523 Open
Capacity of the Gaussian relay channel with independent receiver noises
IT · AIM Open Applied Problems · channel capacity · Gaussian channels · relay channels
OP-00524 Open
Global attraction for Wright-type delayed feedback
DS · AIM Open Applied Problems · delay differential equations · Schwarzian derivatives · Wright's equation
OP-00525 Open
Generic stabilization by static output feedback
OC · AIM Open Applied Problems · linear control systems · pole placement · static output feedback
OP-00526 Open
Global null control of a heat equation with cubic growth
OC · AIM Open Applied Problems · blow-up · null controllability · semilinear heat equations
OP-00527 Open
The sharp number of directions illuminating a convex body
MG · AIM Open Applied Problems · convex bodies · homothetic coverings · illumination numbers
OP-00528 Open
Quadratic growth when a Hamiltonian map has infinitely many periodic orbits
SG · AIM Open Applied Problems · Hamiltonian diffeomorphisms · periodic orbits
OP-00529 Open
Exact null control of a harmonically confined kinetic equation from a wedge
OC · AIM Open Applied Problems · hypoelliptic equations · null controllability · Ornstein–Uhlenbeck operators
OP-00530 Open
Global uniqueness from inverse backscattering data
AP · AIM Open Applied Problems · backscattering data · inverse scattering · Schrödinger operators
OP-00531 Partially resolved
An irrational polygon with nonergodic billiard flow
DS · AIM Open Applied Problems · ergodicity · polygonal billiards
OP-00532 Open
The minimum-area universal cover of planar diameter-one sets
MG · AIM Open Applied Problems · sets of constant width · universal covers
OP-00533 Open
Local scalar geodesic tomography on smooth surfaces
DG · AIM Open Applied Problems · geodesic X-ray transforms · geometric inverse problems · integral geometry
OP-00534 Open
Small-time global null control of no-slip Navier–Stokes flow
OC · AIM Open Applied Problems · Navier–Stokes equations · null controllability
OP-00535 Open
Marked length rigidity in negative curvature
DG · AIM Open Applied Problems · closed geodesics · marked length spectrum · negative curvature
OP-00536 Open
Minimum-time eradication of an expanding set inside a geographic barrier
OC · AIM Open Applied Problems · eradication strategies · moving sets · sets of finite perimeter
OP-00537 Solution claimed
Logarithmic convexity for two coupled subdiffusion orders
AP · AIM Open Applied Problems · backward problems · logarithmic convexity · time-fractional diffusion equations
OP-00538 Open
The full three-dimensional Newton minimum-resistance problem
OC · AIM Open Applied Problems · concave functions · Newton's problem of minimal resistance · shape optimization
OP-00539 Open
Global conductivity uniqueness for the p-Laplacian in higher dimensions
AP · AIM Open Applied Problems · Calderón problem · Dirichlet-to-Neumann maps · p-Laplace equations
OP-00540 Open
A closed nonplanar totally integrable wire billiard in three-space
DS · AIM Open Applied Problems · integrable billiards · twist maps · wire billiards
OP-00541 Open
Lens rigidity for nontrapping surfaces with conjugate points
DG · AIM Open Applied Problems · conjugate points · lens rigidity · scattering relations
OP-00542 Open
Approximate velocity control of a viscoelastic fluid with prescribed transport
OC · AIM Open Applied Problems · approximate controllability · boundary control · viscoelastic fluids
OP-00543 Open
Are all totally integrable outer-length billiards ellipses?
DS · AIM Open Applied Problems · integrable billiards · outer length billiards
OP-00544 Open
Unique continuation for the higher-dimensional p-Laplace equation
AP · AIM Open Applied Problems · p-harmonic functions · unique continuation
OP-00545 Open
Invertibility of the Pestov–Uhlmann reconstruction operator
DG · AIM Open Applied Problems · geodesic X-ray transforms · inversion formulas · simple surfaces
OP-00546 Open
Simultaneously recover sound speed and initial pressure
AP · AIM Open Applied Problems · photoacoustic tomography · sound speeds · wave equations
OP-00547 Open
The near-linear bound for planar halving lines
CO · AIM Open Applied Problems · halving lines · k-sets · planar point sets
OP-00548 Open
Polynomial-time detection below the planted-clique square-root threshold
ST · AIM Open Applied Problems · computational lower bounds · planted cliques · random graphs
OP-00549 Open
Positive metric entropy for billiards arbitrarily close to an ellipse
DS · AIM Open Applied Problems · convex billiards · metric entropy
OP-00550 Open
Saari's constant-inertia conjecture for planar gravitation
DS · AIM Open Applied Problems · celestial mechanics · n-body problems · relative equilibria
OP-00551 Solution claimed
Sharp exponential cost of fast boundary quantum control
OC · AIM Open Applied Problems · control costs · null controllability · Schrödinger equations
OP-00552 Solution claimed
Rigidity of a totally integrable Minkowski billiard in its own unit ball
DS · AIM Open Applied Problems · integrable billiards · Minkowski billiards · twist maps
OP-00553 Open
The exact zero-error Shannon capacity of the seven-cycle
CO · AIM Open Applied Problems · Shannon capacity · strong graph products · zero-error codes
OP-00554 Open
Exact minimum length of an opaque barrier for a square
MG · AIM Open Applied Problems · barriers · opaque sets
OP-00555 Open
The shortest space curve of prescribed minimum width
MG · AIM Open Applied Problems · escape paths · space curves · width
OP-00556 Open
Boundary rigidity of simple manifolds in dimensions at least three
DG · AIM Open Applied Problems · boundary rigidity · simple manifolds · travel-time tomography
OP-00557 Open
Minimal filling volume of a simple manifold
DG · AIM Open Applied Problems · boundary distance functions · minimal fillings
OP-00558 Open
Polynomial-time solution of simple stochastic games
OC · AIM Open Applied Problems · computational complexity · simple stochastic games · stochastic games
OP-00559 Open
Determine a smooth sound-soft obstacle from one far-field pattern
AP · AIM Open Applied Problems · far-field patterns · Helmholtz equation · inverse obstacle scattering
OP-00560 Open
Small-time global control of a slightly superlinear heat equation
AP · AIM Open Applied Problems · blow-up · null controllability · semilinear heat equations
OP-00561 Open
Existence of a flexible closed C² surface in three-space
DG · AIM Open Applied Problems · flexible surfaces · isometric deformations · rigidity
OP-00562 Open
Classify noninjectivity sets of spherical mean tomography
AP · AIM Open Applied Problems · harmonic polynomials · injectivity sets · spherical means
OP-00563 Open
The sharp degree bound for strong edge-colouring
CO · AIM Open Applied Problems · Erdős–Nešetřil conjecture · strong chromatic index · strong edge-colourings
OP-00564 Open
Circular rigidity of totally integrable strong-field magnetic billiards
DS · AIM Open Applied Problems · integrable billiards · magnetic billiards
OP-00565 Open
Solenoidal injectivity of the geodesic ray transform on 2-tensors
DG · AIM Open Applied Problems · geodesic ray transforms · simple manifolds · tensor tomography
OP-00566 Open
Non-Abelian ray transform for simple Gaussian thermostats
DG · AIM Open Applied Problems · Gaussian thermostats · geometric inverse problems · non-Abelian ray transforms
OP-00567 Open
Matheron’s covariogram uniqueness problem in three dimensions
MG · AIM Open Applied Problems · convex bodies · covariograms · phase retrieval
OP-00568 Open
Broken-ray tomography with two smooth convex obstacles
AP · AIM Open Applied Problems · broken ray transforms · integral geometry · reflecting obstacles
OP-00569 Open
A data-independent time for global control of the defocusing cubic wave
OC · AIM Open Applied Problems · exact controllability · semilinear wave equations
OP-00570 Open
Exact optimal control in the scalar Witsenhausen benchmark
OC · AIM Open Applied Problems · team decision problems · Witsenhausen's counterexample
OP-00571 Solution claimed
Interior bounds for stable elliptic states with sign-changing reaction laws
AP · AIM Open Applied Problems · semilinear elliptic equations · stable solutions
OP-00572 Open
Fast dynamo action of the unit ABC flow
AP · ABC flows · AIM Open Applied Problems · fast dynamos
OP-00573 Open
Fourier’s law for a boundary-thermostated anharmonic chain
PR · AIM Open Applied Problems · anharmonic chains · heat conduction · nonequilibrium steady states
OP-00574 Open
Strict physicality for anisotropic singular Q-tensor minimizers
AP · AIM Open Applied Problems · Landau–de Gennes theory · Q-tensors · singular potentials
OP-00575 Open
Existence of an optimal asymmetric Bloch wall of prescribed angle
AP · AIM Open Applied Problems · domain walls · micromagnetics
OP-00576 Open
The optimal three-dimensional quadratic quantization constant
OC · AIM Open Applied Problems · centroidal Voronoi tessellations · lattice quantizers · optimal quantization
OP-00577 Open
Hard-sphere Boltzmann shock profiles at arbitrary Mach number
AP · AIM Open Applied Problems · Boltzmann equation · kinetic theory · shock profiles
OP-00578 Open
Bressan's logarithmic lower bound on the cost of mixing
AP · AIM Open Applied Problems · incompressible flows · mixing · transport equations
OP-00579 Open
Global classical continuation in the chemotaxis-consumption system
AP · AIM Open Applied Problems · chemotaxis-consumption systems · global classical solutions
OP-00580 Open
Finitely many radius sets for compact sphere packings
MG · AIM Open Applied Problems · compact packings · sphere packings
OP-00581 Open
Global attraction for complex-balanced reaction–diffusion with boundary equilibria
AP · AIM Open Applied Problems · chemical reaction networks · convergence to equilibrium · reaction–diffusion systems
OP-00582 Open
Global finite-energy compressible flow at the diatomic exponent
AP · AIM Open Applied Problems · compressible Navier–Stokes equations · weak solutions
OP-00583 Open
Higher regularity for concave stable nonlocal equations
AP · AIM Open Applied Problems · Bellman equations · fully nonlinear integro-differential equations
OP-00584 Open
A single blow-up point for singular extremal states on convex domains
AP · AIM Open Applied Problems · extremal solutions · singular sets
OP-00585 Open
One cubic NLS trajectory with unbounded Sobolev norm
AP · AIM Open Applied Problems · energy cascades · nonlinear Schrödinger equations
OP-00586 Open
Competitive exclusion by the slowest diffuser in a multispecies habitat
AP · AIM Open Applied Problems · competitive exclusion · evolution of dispersal · reaction-diffusion systems
OP-00587 Open
Do finite-energy elastic minimizers satisfy force balance?
AP · AIM Open Applied Problems · Euler–Lagrange equations · nonlinear elasticity · polyconvexity
OP-00588 Open
The attainable stiffness tensors of two-phase elastic composites
AP · AIM Open Applied Problems · composite materials · G-closures · homogenization
OP-00589 Open
Giga’s embedded curve-diffusion conjecture
AP · AIM Open Applied Problems · curve diffusion flow · embedded curves · geometric evolution equations
OP-00590 Open
Global regularity of the planar noncorotational FENE fluid
AP · AIM Open Applied Problems · FENE dumbbell model · Fokker–Planck equations · polymeric fluids
OP-00591 Open
Weak uniqueness for fourth-order aggregation–diffusion
AP · aggregation-diffusion equations · AIM Open Applied Problems · thin-film equations · Wasserstein gradient flows
OP-00592 Open
Hölder regularity for nondivergence kinetic jump equations
AP · AIM Open Applied Problems · Hölder estimates · integro-differential equations · kinetic equations
OP-00593 Open
Flatness of three-dimensional fractional minimizing cones for every interaction order
AP · AIM Open Applied Problems · fractional perimeters · minimal cones · nonlocal minimal surfaces
OP-00594 Open
Instantaneous spreading for fractional-pressure flow in several dimensions
AP · AIM Open Applied Problems · fractional pressure · infinite speed of propagation · porous medium equations
OP-00595 Open
Multidimensional weak uniqueness for porous-medium flow with fractional pressure
AP · AIM Open Applied Problems · fractional pressure · porous medium equations · uniqueness of weak solutions
OP-00596 Open
Bounded-Hessian Liouville rigidity in dimensions three and four
AP · AIM Open Applied Problems · fully nonlinear elliptic equations · Liouville theorems
OP-00597 Open
Uniqueness of Glimm–Lax solutions for arbitrarily rough bounded data
AP · AIM Open Applied Problems · entropy solutions · hyperbolic conservation laws
OP-00598 Open
Rigidity of positively curved shells above one-half Hölder regularity
DG · AIM Open Applied Problems · convex integration · convex surfaces · isometric embeddings
OP-00599 Open
Global regularity of two-dimensional ideal incompressible MHD
AP · AIM Open Applied Problems · global regularity · incompressible flows · magnetohydrodynamics
OP-00600 Open
The exact minimum ropelength of a trefoil
GT · AIM Open Applied Problems · ideal knots · ropelength
OP-00601 Open
Uniqueness of the homogeneous cooling state for inelastic hard spheres
AP · AIM Open Applied Problems · granular gases · inelastic Boltzmann equations · self-similar solutions
OP-00602 Open
Large-data global smoothness for the spatially inhomogeneous Boltzmann equation
AP · AIM Open Applied Problems · Boltzmann equation · classical solutions · kinetic equations
OP-00603 Open
Smooth unforced inviscid Boussinesq evolution on the whole plane
AP · AIM Open Applied Problems · Boussinesq equations · finite-time blowup · global regularity
OP-00604 Open
Quantization of radial finite-time collapse in fully parabolic Keller–Segel
AP · AIM Open Applied Problems · chemotactic collapse · finite-time blow-up · Keller–Segel system
OP-00605 Open
The three-dimensional lattice-periodic Kelvin problem
AP · AIM Open Applied Problems · Kelvin problem · lattice tilings · minimal partitions
OP-00606 Open
A length-independent mean energy bound for Kuramoto–Sivashinsky
AP · AIM Open Applied Problems · energy bounds · Kuramoto–Sivashinsky equation · spatiotemporal chaos
OP-00607 Open
Are bounded ancient Landau–Coulomb distributions necessarily Maxwellians?
AP · AIM Open Applied Problems · ancient solutions · Landau equation · Liouville theorems
OP-00608 Open
Landau–Coulomb smoothing controlled only by macroscopic quantities
AP · AIM Open Applied Problems · Landau equation · regularization estimates
OP-00609 Open
The bulk ground-state energy of the planar Lennard–Jones system
MP · AIM Open Applied Problems · crystallization · lattice energies · Lennard–Jones potentials
OP-00610 Open
The three-dimensional steady Leray problem with unrestricted boundary fluxes
AP · AIM Open Applied Problems · Leray problem · Navier–Stokes equations · steady flows
OP-00611 Open
Global weak flow of three-dimensional nematic directors without a hemisphere restriction
AP · AIM Open Applied Problems · Ericksen–Leslie system · nematic liquid crystals · weak solutions
OP-00612 Open
Instantaneous strict separation for three-dimensional local Cahn–Hilliard
AP · AIM Open Applied Problems · Cahn–Hilliard equations · logarithmic potentials · strict separation
OP-00613 Open
Uniqueness of all weak dual solutions of fractional porous-medium flow
AP · AIM Open Applied Problems · fractional porous medium equations · Riemannian manifolds · weak dual solutions
OP-00614 Open
Global classical Maxwell–Stefan diffusion with arbitrary pair friction
AP · AIM Open Applied Problems · cross-diffusion systems · gas mixtures · Maxwell–Stefan equations
OP-00615 Open
Nonlinear Landau damping near a Maxwellian on the whole space
AP · AIM Open Applied Problems · Landau damping · Vlasov–Poisson equations
OP-00616 Open
Regular MEMS extremal states without an asymptotic curvature condition
AP · AIM Open Applied Problems · extremal solutions · singular nonlinearities
OP-00617 Open
Does a bounded interface slope prevent two-phase Muskat singularities?
AP · AIM Open Applied Problems · free boundaries · Muskat problem · porous media
OP-00618 Open
Global regularity of the three-dimensional Navier–Stokes equations
AP · AIM Open Applied Problems · global regularity · incompressible flows · Navier–Stokes equations
OP-00619 Open
Attainment of the three-dimensional neo-Hookean energy in the regular admissible class
AP · AIM Open Applied Problems · existence of minimizers · neo-Hookean materials · nonlinear elasticity
OP-00620 Open
The no-slip inviscid limit in two dimensions
AP · AIM Open Applied Problems · boundary layers · inviscid limits · Navier–Stokes equations
OP-00621 Open
Large-data global regularity for creeping-flow Oldroyd–B without stress diffusion
AP · AIM Open Applied Problems · global regularity · Oldroyd-B fluids · viscoelastic fluids
OP-00622 Open
Vanishing nonlinear viscosity without commuting transport and diffusion matrices
AP · AIM Open Applied Problems · BV solutions · hyperbolic conservation laws · vanishing viscosity
OP-00623 Open
Automatic conservation laws for renormalized nonlinear diffusion
AP · AIM Open Applied Problems · conservation laws · reaction–diffusion systems · renormalized solutions
OP-00624 Open
Optimal nonlocal obstacle regularity with a minimally smooth obstacle
AP · AIM Open Applied Problems · integro-differential operators · obstacle problems · optimal stopping
OP-00625 Open
Soliton resolution for bounded nonradial energy-critical waves
AP · AIM Open Applied Problems · energy-critical wave equations · soliton resolution
OP-00626 Open
Global regularity of viscous planar MHD without magnetic diffusion
AP · AIM Open Applied Problems · global regularity · magnetohydrodynamics
OP-00627 Open
Large-data weak solutions for three-dimensional stress-diffusive Oldroyd-B flow
AP · AIM Open Applied Problems · Oldroyd-B model · viscoelastic fluids · weak solutions
OP-00628 Open
Axisymmetry of equilibrium distributions for Onsager rods
AP · AIM Open Applied Problems · nematic liquid crystals · Onsager model
OP-00629 Open
Finiteness of interior defects in Oseen–Frank minimizers
AP · AIM Open Applied Problems · nematic liquid crystals · Oseen–Frank energy · point defects
OP-00630 Open
Strong comparison for ordered p-harmonic fields
AP · AIM Open Applied Problems · comparison principles · p-harmonic functions
OP-00631 Open
Finite-time growth of total variation in physical gas dynamics
AP · AIM Open Applied Problems · entropy solutions · hyperbolic conservation laws
OP-00632 Open
Asymptotic stability of the phi-four kink without odd symmetry
AP · AIM Open Applied Problems · asymptotic stability · kinks · scalar field equations
OP-00633 Open
Finite-time collapse in the planar self-steepening Schrödinger equation
AP · AIM Open Applied Problems · derivative nonlinear Schrödinger equations · finite-time blow-up
OP-00634 Open
Existence of elastic equilibria under quasiconvexity and infinite compression energy
AP · AIM Open Applied Problems · calculus of variations · nonlinear elasticity · quasiconvexity
OP-00635 Open
The densest packing of congruent regular tetrahedra
MG · AIM Open Applied Problems · packing densities · regular tetrahedra
OP-00636 Open
Global classical solutions for repulsive relativistic Vlasov–Poisson
AP · AIM Open Applied Problems · collisionless plasmas · Vlasov–Poisson systems
OP-00637 Open
Global classical continuation for a reversible mass-action reaction
AP · AIM Open Applied Problems · mass-action kinetics · reaction–diffusion systems
OP-00638 Open
Bounded variation of gradients in the Rudin–Osher–Fatemi denoising model
AP · AIM Open Applied Problems · functions of bounded variation · total variation minimizers
OP-00639 Open
Hölder regularity under directional nonlocal ellipticity alone
AP · AIM Open Applied Problems · Hölder estimates · integro-differential equations · jump processes
OP-00640 Open
Global smoothness for the real scalar defocusing septic wave equation
AP · AIM Open Applied Problems · energy-supercritical equations · finite-time blow-up · nonlinear wave equations
OP-00641 Open
Global smooth Schrödinger maps below the degree-zero energy threshold
AP · AIM Open Applied Problems · energy-critical dispersive equations · Landau–Lifshitz equation · Schrödinger maps
OP-00642 Open
Sharp gradient regularity for higher-dimensional p-Poisson equations
AP · AIM Open Applied Problems · gradient regularity · p-Laplace equations
OP-00643 Open
Nonlinear orbital stability of small solitary gravity waves
AP · AIM Open Applied Problems · orbital stability · solitary waves · water waves
OP-00644 Open
The quadruple-bubble conjecture in three-dimensional space
DG · AIM Open Applied Problems · isoperimetric clusters · soap bubbles
OP-00645 Open
Optimal dimension for bounded subquadratic p-Laplace extremal states
AP · AIM Open Applied Problems · extremal solutions · p-Laplace equations
OP-00646 Open
Global regularity for supercritical dissipative surface quasi-geostrophic flow
AP · AIM Open Applied Problems · fractional dissipation · global regularity · quasi-geostrophic equations
OP-00647 Open
Global smoothness of the one-dimensional surface-growth equation
AP · AIM Open Applied Problems · fourth-order parabolic equations · global regularity · surface growth models
OP-00648 Open
Preservation of strict positivity for the cubic thin-film equation
AP · AIM Open Applied Problems · degenerate parabolic equations · thin-film equations
OP-00649 Open
Barenblatt attraction for porous-medium diffusion with time memory
AP · AIM Open Applied Problems · Caputo derivatives · large-time behaviour · porous medium equations
OP-00650 Open
Uniqueness for a point source in time-fractional porous-medium flow
AP · AIM Open Applied Problems · Caputo derivatives · fundamental solutions · porous medium equations
OP-00651 Open
Largest radius ratio in nonuniform triangulated circle packings
MG · AIM Open Applied Problems · circle packings · triangulations
OP-00652 Open
Global regularity for two-dimensional Kuramoto–Sivashinsky on arbitrary square tori
AP · AIM Open Applied Problems · global regularity · growing modes · Kuramoto–Sivashinsky equation
OP-00653 Open
The ball as the least densely packable convex solid
MG · AIM Open Applied Problems · convex bodies · Kepler conjecture · packing densities
OP-00654 Open
Self-sustained oscillations in the full voltage–conductance neuron equation
AP · AIM Open Applied Problems · kinetic equations · neural networks · periodic solutions
OP-00655 Open
Finite-time singularity formation for unconstrained Willmore flow
DG · AIM Open Applied Problems · finite-time singularities · geometric flows · Willmore flow
OP-00656 Open
Scattering of arbitrary small energy data for the three-dimensional Zakharov system
AP · AIM Open Applied Problems · dispersive equations · scattering · Zakharov system
OP-00657 Open
Finite-time Langmuir collapse for the three-dimensional Zakharov system
AP · AIM Open Applied Problems · blow-up · Langmuir waves · Zakharov system
OP-00658 Solution claimed
Global optimality of the Abrikosov triangular lattice
AP · Abrikosov lattice · AIM Open Applied Problems · Coulomb gases · renormalized energy
OP-00659 Solution claimed
Absence of doubly infinite minimizing paths in planar first-passage percolation
PR · AIM Open Applied Problems · bigeodesics · first-passage percolation
OP-00660 Solution claimed
Affine Bernstein rigidity in dimensions three through nine
AP · affine maximal hypersurfaces · AIM Open Applied Problems · Bernstein problem · fourth-order elliptic equations
OP-00661 Solution claimed
Can entangled codewords improve amplitude-damping classical capacity?
MP · AIM Open Applied Problems · amplitude damping channel · classical capacity · Holevo information
OP-00662 Solution claimed
Logarithmic controlled bandwidth for locally analytic functions
NA · AIM Open Applied Problems · bandlimited approximation · Levin method · oscillatory integrals
OP-00663 Solution claimed
Extended states in the three-dimensional Anderson model
SP · absolutely continuous spectrum · AIM Open Applied Problems · Anderson model · random Schrödinger operators
OP-00664 Solution claimed
Calderón uniqueness from an arbitrary local boundary patch
AP · AIM Open Applied Problems · Calderón problem · inverse conductivity problem · partial data
OP-00665 Solution claimed
Smooth approximation of three-dimensional Sobolev homeomorphisms
FA · AIM Open Applied Problems · diffeomorphic approximation · nonlinear elasticity · Sobolev homeomorphisms
OP-00666 Solution claimed
Global Birkhoff billiard integrability conjecture
DS · AIM Open Applied Problems · Birkhoff conjecture · caustics · convex billiards
OP-00667 Solution claimed
Sharp Bochner–Riesz summability in three dimensions
CA · AIM Open Applied Problems · Bochner–Riesz means · Fourier multipliers
OP-00668 Solution claimed
Can every bounded entire Burgers profile recur at late times?
AP · AIM Open Applied Problems · Cole–Hopf transformation · omega-limit sets · viscous Burgers equation
OP-00669 Solution claimed
Euclidean isoperimetry in higher-dimensional Cartan–Hadamard manifolds
DG · AIM Open Applied Problems · Cartan–Hadamard manifolds · isoperimetric inequality · nonpositive curvature
OP-00670 Solution claimed
Bounded harmonic lifting for complex media
AP · AIM Open Applied Problems · complex elliptic operators · harmonic lifting · maximum principle
OP-00671 Solution claimed
Minimum number of continuous adaptive measurements for vector recovery
NA · adaptive algorithms · AIM Open Applied Problems · continuous measurements · information-based complexity
OP-00672 Solution claimed
The cost of continuous reconstruction on Banach unit balls
NA · AIM Open Applied Problems · continuous measurements · information-based complexity · manifold widths
OP-00673 Solution claimed
Absence of an infinite cluster at criticality in three-dimensional percolation
PR · AIM Open Applied Problems · critical phenomena · percolation
OP-00674 Solution claimed
One-dimensionality of monotone Allen–Cahn fronts in dimension five
AP · AIM Open Applied Problems · Allen–Cahn equation · De Giorgi conjecture · phase transitions
OP-00675 Solution claimed
A genuinely periodic firing pattern in the delayed noisy integrate-and-fire PDE
AP · AIM Open Applied Problems · integrate-and-fire neurons · nonlinear Fokker–Planck equations · periodic solutions
OP-00676 Solution claimed
Dixmier’s unitarizability problem for countable groups
FA · AIM Open Applied Problems · amenability · uniformly bounded representations · unitarizable groups
OP-00677 Solution claimed
Monotone variance in the Gaussian approximation to DrMMD flow
PR · AIM Open Applied Problems · Gaussian approximation · kernel gradient flows · maximum mean discrepancy
OP-00678 Solution claimed
Poisson kernel bounds for elliptic boundary diffusion on Lipschitz domains
AP · AIM Open Applied Problems · Dirichlet-to-Neumann operator · heat kernel bounds · Lipschitz domains
OP-00679 Solution claimed
Absolute continuity of stationary Elo ratings
PR · AIM Open Applied Problems · Elo rating system · invariant measures · Markov chains
OP-00680 Solution claimed
The entropy photon-number inequality
MP · AIM Open Applied Problems · bosonic channels · entropy photon-number inequality · von Neumann entropy
OP-00681 Solution claimed
Sharp local smoothing for the three-dimensional wave equation
AP · AIM Open Applied Problems · Fourier integral operators · local smoothing · wave equation
OP-00682 Solution claimed
Smooth-gradient approximation of finite-Fisher-information scores
AP · AIM Open Applied Problems · Fisher information · optimal transport · weighted Sobolev approximation
OP-00683 Solution claimed
Almost-everywhere Fourier reconstruction of L log L signals
CA · AIM Open Applied Problems · almost everywhere convergence · Carleson operator · Fourier series
OP-00684 Solution claimed
Full-space minimizers for subcritical fourth-order aggregation energy
AP · aggregation-diffusion equations · AIM Open Applied Problems · energy minimizers
OP-00685 Solution claimed
Logarithmic convexity for subdiffusion with non-gradient drift
AP · AIM Open Applied Problems · backward problems · logarithmic convexity · time-fractional diffusion
OP-00686 Solution claimed
Variance ordering for Gaussian alpha-divergence approximations
PR · AIM Open Applied Problems · factorized Gaussian approximations · variational inference · α-divergences
OP-00687 Solution claimed
A uniform gap for the spin-one Heisenberg chain
MP · AIM Open Applied Problems · Haldane gap · Heisenberg chain · quantum spin chains
OP-00688 Solution claimed
A fixed-time lower bound for Trotter splitting of the hydrogen ground state
NA · AIM Open Applied Problems · Coulomb potential · splitting methods · Trotter product formula
OP-00689 Solution claimed
Finite-density time sampling of an infinite observation window
FA · AIM Open Applied Problems · Beurling density · dynamical sampling · frames
OP-00690 Solution claimed
Continuous gradients for three-dimensional infinity-harmonic functions
AP · AIM Open Applied Problems · gradient regularity · infinity Laplacian · viscosity solutions
OP-00691 Solution claimed
Uniform spatial stability of von Neumann algebras
OA · AIM Open Applied Problems · Kadison–Kastler conjecture · perturbations of von Neumann algebras
OP-00692 Solution claimed
Kadison’s similarity problem
OA · AIM Open Applied Problems · C*-algebras · completely bounded maps · similarity problem
OP-00693 Solution claimed
Nonexistence of subcritical Lane–Emden equilibria in higher dimensions
AP · AIM Open Applied Problems · Lane–Emden systems · Liouville theorems
OP-00694 Solution claimed
Global attraction in D-stable Lotka–Volterra systems
DS · AIM Open Applied Problems · D-stability · global stability · Lotka-Volterra systems
OP-00695 Solution claimed
The symmetric Mahler inequality in four dimensions
MG · AIM Open Applied Problems · convex bodies · Mahler conjecture · volume product
OP-00696 Solution claimed
Optimal uniform observation time for mixed finite element waves
NA · AIM Open Applied Problems · boundary observability · mixed finite elements · wave equation
OP-00697 Solution claimed
The modified integer round-up conjecture for cutting stock
OC · AIM Open Applied Problems · bin packing · cutting stock problem · integrality gap
OP-00698 Solution claimed
Continuity of manifold transport under MTW and convex injectivity domains
AP · AIM Open Applied Problems · Ma–Trudinger–Wang condition · optimal transport · Riemannian manifolds
OP-00699 Solution claimed
The maximum number of mutually unbiased bases in dimension six
CO · AIM Open Applied Problems · complex Hadamard matrices · mutually unbiased bases
OP-00700 Solution claimed
A nonuniqueness phase on every nonamenable transitive graph
PR · AIM Open Applied Problems · nonamenable graphs · percolation · uniqueness threshold
OP-00701 Solution claimed
Does directional ellipticity force a fractional energy bound?
AP · AIM Open Applied Problems · coercivity estimates · fractional Sobolev spaces · integro-differential operators
OP-00702 Solution claimed
Removing the logarithmic loss in Helmholtz Nyström estimates
NA · AIM Open Applied Problems · boundary integral equations · Helmholtz equation · Nyström method
OP-00703 Solution claimed
The first dimension with a singular one-phase minimizing cone
AP · AIM Open Applied Problems · Alt–Caffarelli functional · minimizing cones · one-phase free boundary problem
OP-00704 Solution claimed
Hot spots on convex planar domains
SP · AIM Open Applied Problems · convex domains · hot spots conjecture · Neumann eigenfunctions
OP-00705 Solution claimed
Polynomial sample complexity for deletion-trace reconstruction
PR · AIM Open Applied Problems · deletion channel · sample complexity · trace reconstruction
OP-00706 Solution claimed
Composing two PPT channels destroys all entanglement
MP · AIM Open Applied Problems · completely positive maps · entanglement breaking channels · PPT squared conjecture
OP-00707 Solution claimed
Small-ball ratios for general symmetric product priors
PR · AIM Open Applied Problems · Onsager–Machlup functionals · product measures · small-ball probabilities
OP-00708 Solution claimed
A uniform limit-cycle bound for quadratic planar dynamics
DS · AIM Open Applied Problems · Hilbert's sixteenth problem · limit cycles · quadratic vector fields
OP-00709 Solution claimed
No asymptotic extinction in bounded weakly reversible mass-action kinetics
DS · AIM Open Applied Problems · chemical reaction networks · mass-action kinetics · persistence
OP-00710 Solution claimed
Uniqueness of entropy-admissible renormalized Boltzmann solutions
AP · AIM Open Applied Problems · Boltzmann equation · renormalized solutions · uniqueness
OP-00711 Solution claimed
The Robin fundamental gap conjecture
SP · AIM Open Applied Problems · convex domains · fundamental gap · Robin Laplacian
OP-00712 Solution claimed
Calderón uniqueness for bounded measurable conductivities
AP · AIM Open Applied Problems · Calderón problem · Dirichlet-to-Neumann map · electrical impedance tomography
OP-00713 Solution claimed
The directional zero–one law in three-dimensional random media
PR · AIM Open Applied Problems · random walk in random environment · zero–one laws
OP-00714 Solution claimed
Does directional transience imply ballistic transport in an iid medium?
PR · AIM Open Applied Problems · ballisticity · random walk in random environment
OP-00715 Solution claimed
Sidorenko's lower bound for bipartite homomorphism counts
CO · AIM Open Applied Problems · graph homomorphisms · Sidorenko's conjecture
OP-00716 Solution claimed
Simplices maximize the isotropic constant
MG · AIM Open Applied Problems · convex bodies · isotropic constant · slicing problem
OP-00717 Solution claimed
Smooth anisotropic Calderón uniqueness
AP · AIM Open Applied Problems · Calderón problem · Dirichlet-to-Neumann map · Riemannian manifolds
OP-00718 Solution claimed
Sharp Fourier extension from the sphere in three dimensions
CA · AIM Open Applied Problems · extension operator · Fourier restriction · sphere
OP-00719 Solution claimed
Cardy's crossing formula for square-lattice bond percolation
PR · AIM Open Applied Problems · conformal invariance · critical percolation · crossing probabilities
OP-00720 Solution claimed
Positive metric entropy for a standard map
DS · AIM Open Applied Problems · Lyapunov exponents · metric entropy · standard map
OP-00721 Solution claimed
Recover both Lamé moduli from static boundary measurements
AP · AIM Open Applied Problems · inverse problems · Lamé parameters · linear elasticity
OP-00722 Solution claimed
Stein’s Hilbert-transform bound along Lipschitz directions
CA · AIM Open Applied Problems · directional Hilbert transform · Lipschitz vector fields · singular integrals
OP-00723 Solution claimed
Linear growth of interior Steklov nodal volume
SP · AIM Open Applied Problems · nodal sets · Steklov eigenfunctions · Yau's conjecture
OP-00724 Solution claimed
Exponential interior decay for smooth Steklov domains
SP · AIM Open Applied Problems · interior decay · Steklov eigenfunctions
OP-00725 Solution claimed
Strict convexity of the planar exponential first-passage shape
PR · AIM Open Applied Problems · first-passage percolation · limit shapes
OP-00726 Solution claimed
Strong thin-tree conjecture
CO · AIM Open Applied Problems · edge connectivity · spanning trees · thin trees
OP-00727 Solution claimed
Bose condensation at fixed dilute density
MP · AIM Open Applied Problems · Bose-Einstein condensation · dilute Bose gases · thermodynamic limit
OP-00728 Solution claimed
Exact complexity of unit-job precedence scheduling on three processors
OC · AIM Open Applied Problems · computational complexity · makespan · precedence-constrained scheduling
OP-00729 Solution claimed
A uniform L3 estimate for the triangular Hilbert transform
CA · AIM Open Applied Problems · multilinear singular integrals · triangular Hilbert transform
OP-00730 Solution claimed
Gaussian-energy optimality of the triangular lattice among periodic configurations
MG · AIM Open Applied Problems · Gaussian energy · triangular lattice · universal optimality
OP-00731 Solution claimed
An area law for general gapped two-dimensional spin systems
MP · AIM Open Applied Problems · area law · entanglement entropy · gapped ground states
OP-00732 Solution claimed
Uniform boundedness of the first atomic ionization energy
SP · AIM Open Applied Problems · Coulomb systems · ionization conjecture · many-body Schrödinger operators
OP-00733 Solution claimed
The Unique Games Conjecture
CO · AIM Open Applied Problems · constraint satisfaction · hardness of approximation · Unique Games Conjecture
OP-00734 Solution claimed
A discrete Aronson–Bénilan estimate for an upwind growth scheme
NA · AIM Open Applied Problems · Aronson–Bénilan estimate · porous medium equation · upwind schemes
OP-00735 Solution claimed
Triangle inequality for the pullback distance of verbose persistence barcodes
AT · AIM Open Applied Problems · persistent homology · verbose barcodes · Vietoris–Rips complexes
OP-00736 Solution claimed
Villani’s convex-injectivity-domain conjecture
DG · AIM Open Applied Problems · injectivity domains · Ma–Trudinger–Wang condition · optimal transport
OP-00737 Solution claimed
Large-data global classical solutions of relativistic Vlasov–Maxwell
AP · AIM Open Applied Problems · global classical solutions · kinetic theory · Vlasov–Maxwell system
OP-00738 Solution claimed
Yau's sharp upper bound for nodal volume
SP · AIM Open Applied Problems · Laplace eigenfunctions · nodal sets · Yau's conjecture
OP-00739 Solution claimed
Path connectivity of the infinity Z-Gromov–Wasserstein space
MG · AIM Open Applied Problems · Gromov–Wasserstein distance · measure networks · path connectedness
OP-00740 Solution claimed
Polynomial growth of reachable neighborhoods for analytic control systems
OC · AIM Open Applied Problems · analytic control systems · reachable sets · small-time local controllability
OP-00741 Solution claimed
A mixed Sobolev estimate for reconstructing a scalar potential
AP · AIM Open Applied Problems · Bourgain–Brezis estimates · divergence equation · fractional Sobolev spaces
OP-00742 Solution claimed
Exact uniform control time near a viscous Burgers shock
AP · AIM Open Applied Problems · Burgers equation · null controllability · vanishing viscosity
OP-00743 Solution claimed
Interior smoothness of carrying simplices in competitive population maps
DS · AIM Open Applied Problems · carrying simplex · competitive maps · invariant manifolds
OP-00744 Solution claimed
Analytic boundary diffusion on continuous functions for Lipschitz domains
FA · AIM Open Applied Problems · Dirichlet-to-Neumann operator · holomorphic semigroups · Lipschitz domains
OP-00745 Solution claimed
Entropy chain rule on nonsmooth nonconvex Lipschitz domains
AP · AIM Open Applied Problems · Fisher information · Fokker–Planck equation · relative entropy
OP-00746 Solution claimed
Observability of an acoustic shell at equal bulk and surface speeds
OC · AIM Open Applied Problems · dynamic boundary conditions · observability · wave equation
OP-00747 Solution claimed
Universal identities for Euclidean mechanical Lie brackets
RA · AIM Open Applied Problems · free Lie algebras · Poisson brackets · splitting methods
OP-00748 Solution claimed
Extending a symmetric one-dependent four-color law across a branch
PR · AIM Open Applied Problems · finitely dependent processes · proper colorings · star graphs
OP-00749 Solution claimed
Full Sobolev invertibility range for Hausdorff-measure screen operators
NA · AIM Open Applied Problems · boundary element methods · fractal screens · single-layer operator
OP-00750 Solution claimed
Local potential bases on Freudenthal meshes
NA · AIM Open Applied Problems · finite elements · Freudenthal meshes · Stokes complex
OP-00751 Solution claimed
Fourth-order diffusion approximation for three-player ruin
PR · AIM Open Applied Problems · diffusion approximation · gambler's ruin · harmonic measure
OP-00752 Solution claimed
Global constrained null control of a two-phase Stefan interface
OC · AIM Open Applied Problems · free boundary problems · null controllability · Stefan problem
OP-00753 Solution claimed
Consistency of the Greedy Sparsest Poset algorithm
ST · AIM Open Applied Problems · causal discovery · latent variables · maximal ancestral graphs
OP-00754 Solution claimed
Sharp interactive privacy rates for spectral density estimation
ST · AIM Open Applied Problems · local differential privacy · minimax rates · spectral density estimation
OP-00755 Solution claimed
Universality of the interleaving distance over arbitrary fields
AT · AIM Open Applied Problems · interleaving distance · multiparameter persistence · stability
OP-00756 Solution claimed
Uniform covariance bounds for constrained Ising replicas
PR · AIM Open Applied Problems · canonical ensembles · covariance bounds · Ising model
OP-00757 Solution claimed
A uniform Gaussian approximation bound for Jack measures
PR · AIM Open Applied Problems · Berry–Esseen bounds · Jack measure · Stein's method
OP-00758 Solution claimed
Removing the logarithmic loss in the Li–Wu KdV integrator
NA · AIM Open Applied Problems · error estimates · Korteweg–de Vries equation · low-regularity integrators
OP-00759 Solution claimed
The Mercedes-star partition of a disk
SP · AIM Open Applied Problems · Dirichlet eigenvalues · spectral minimal partitions
OP-00760 Solution claimed
Existence for adaptive porous flow with a negative drag jump
AP · AIM Open Applied Problems · nonmonotone constitutive laws · porous media flow · weak solutions
OP-00761 Solution claimed
Maximal gain from randomization with nonadaptive linear measurements
NA · AIM Open Applied Problems · information-based complexity · linear information · randomized algorithms
OP-00762 Solution claimed
Uniform control of Neumann advection–diffusion for non-gradient flows
OC · AIM Open Applied Problems · null controllability · transport-diffusion equations · vanishing viscosity
OP-00763 Solution claimed
Second-order Sobolev regularity of p-harmonic functions beyond the Cordes range
AP · AIM Open Applied Problems · degenerate elliptic equations · p-Laplace equation · Sobolev regularity
OP-00764 Solution claimed
Boundary control to equilibrium for a parabolic obstacle problem
OC · AIM Open Applied Problems · boundary control · obstacle problem · variational inequalities
OP-00765 Solution claimed
Recover a potential on a general known Riemannian manifold
AP · AIM Open Applied Problems · Calderón problem · Dirichlet-to-Neumann map · inverse problems
OP-00766 Solution claimed
Minimax rates for private density estimation with mixed anisotropy
ST · AIM Open Applied Problems · density estimation · local differential privacy · minimax rates
OP-00767 Solution claimed
Characterizing realizable geodesic scattering data
DG · AIM Open Applied Problems · geometric inverse problems · scattering relation · simple surfaces
OP-00768 Solution claimed
Automorphism-invariant one-dependent colorings of regular trees
PR · AIM Open Applied Problems · finitely dependent processes · proper colorings · regular trees
OP-00769 Solution claimed
The sharp local maneuvering time for a shallow-water tank
OC · AIM Open Applied Problems · local controllability · Saint-Venant equations · water tank
OP-00770 Solution claimed
Sharp characterization of exactly trackable boundary heat fluxes
AP · AIM Open Applied Problems · boundary control · heat equation · tracking controllability
OP-00771 Solution claimed
Sharp local approximation widths for rough elliptic equations
NA · AIM Open Applied Problems · elliptic equations with rough coefficients · Kolmogorov n-widths · multiscale finite element methods
OP-00772 Solution claimed
Boundary observation of a Schrödinger field with slower surface dispersion
OC · AIM Open Applied Problems · dynamic boundary conditions · observability · Schrödinger equation
OP-00773 Solution claimed
Does integration of uniformly derivative-bounded analytic functions suffer the dimensional curse?
NA · AIM Open Applied Problems · curse of dimensionality · information-based complexity · numerical integration
OP-00774 Solution claimed
Sharp asymptotic constant for rational approximation of fractional inverse powers
NA · AIM Open Applied Problems · fractional powers · rational approximation · Stieltjes functions
OP-00775 Solution claimed
Draws in the undirected trapping game on percolation clusters
PR · AIM Open Applied Problems · combinatorial games · site percolation
OP-00776 Solution claimed
Uniqueness of nonnegative heat controls at the minimum time
AP · AIM Open Applied Problems · constrained control · heat equation · minimal control time
OP-00777 Solution claimed
Deciding nonnegativity of unnormalized univariate trace polynomials
AG · AIM Open Applied Problems · decidability · power sums · trace polynomials
OP-00778 Solution claimed
Strong convergence rate of the fractional WIS Euler integrator
NA · AIM Open Applied Problems · fractional Brownian motion · strong convergence · Wick–Itô–Skorohod integral
OP-00779 Solution claimed
Maximal motion-planning complexity of aspherical connected sums
AT · AIM Open Applied Problems · aspherical manifolds · connected sums · topological complexity
OP-00780 Solution claimed
The centre-rank formula for aspherical motion planning
AT · AIM Open Applied Problems · aspherical manifolds · centre of the fundamental group · topological complexity
OP-00781 Solution claimed
Small mod-two area cycles in drawings with bounded pairwise intersections
CO · AIM Open Applied Problems · Heilbronn problems · mod-two cycles · topological graphs
OP-00782 Solution claimed
Positive equilibrium attraction for an irreversible catalytic reaction
AP · AIM Open Applied Problems · chemical reaction networks · convergence to equilibrium · reaction-diffusion systems
OP-00783 Solution claimed
Calderón–Zygmund estimates for general concave nonlocal equations
AP · AIM Open Applied Problems · Bellman equations · fully nonlinear integro-differential equations · Sobolev estimates
OP-00784 Solution claimed
Polynomial decay for KdV with three critical linear modes
AP · AIM Open Applied Problems · critical lengths · decay rates · Korteweg–de Vries equation
OP-00785 Solution claimed
Continuation of the cutoff Boltzmann flow from macroscopic bounds
AP · AIM Open Applied Problems · Boltzmann equation · conditional regularity
OP-00786 Solution claimed
Unconditional uniqueness for entropy-dissipating reaction–diffusion
AP · AIM Open Applied Problems · reaction–diffusion systems · renormalized solutions · uniqueness
OP-00787 Solution claimed
Characterizing discrete sets generated by fixed-parameter extrapolation
MG · AIM Open Applied Problems · aperiodic order · fixed-parameter extrapolation · Pisot numbers
OP-00788 Solution claimed
Relative density of sets generated by fixed-parameter extrapolation
MG · AIM Open Applied Problems · aperiodic order · fixed-parameter extrapolation · relatively dense sets
OP-00789 Solution claimed
An extreme solitary wave for the bidirectional Whitham system
AP · AIM Open Applied Problems · highest waves · solitary waves · Whitham–Boussinesq system
OP-00790 Solution claimed
A bounded number of flat transversals for fat convex sets
MG · AIM Open Applied Problems · fat convex sets · geometric transversals · Helly-type theorems
OP-00791 Solution claimed
The zero center-of-mass diffusion limit for kinetic FENE fluids
AP · AIM Open Applied Problems · dilute polymeric fluids · FENE dumbbell model
OP-00792 Solution claimed
A finite three-ample complex with nontrivial fundamental group
AT · AIM Open Applied Problems · ample simplicial complexes · fundamental group
OP-00793 Solution claimed
Continuity of finite-cluster mass at the onset of Flory gelation
AP · AIM Open Applied Problems · coagulation equations · gelation
OP-00794 Solution claimed
Finite propagation in fourth-order aggregation–diffusion
AP · aggregation-diffusion equations · AIM Open Applied Problems · finite speed of propagation · thin-film equations
OP-00795 Solution claimed
Continuity for degenerate fractional-pressure porous-medium flow
AP · AIM Open Applied Problems · continuity of weak solutions · fractional pressure · porous medium equations
OP-00796 Solution claimed
Optimal obstacle regularity for stable jump kernels with only angular integrability
AP · AIM Open Applied Problems · nonlocal obstacle problems · stable operators
OP-00797 Solution claimed
Counting half-integral polygons with collinear interior lattice points
CO · AIM Open Applied Problems · lattice polygons · rational polygons
OP-00798 Solution claimed
Counting Ehrhart quasipolynomials of half-integral polygons
CO · AIM Open Applied Problems · Ehrhart quasipolynomials · rational polygons
OP-00799 Solution claimed
Ergodicity of higher-dimensional Ising clumps
PR · AIM Open Applied Problems · cubical sets · Markov chains · topology-preserving dynamics
OP-00800 Solution claimed
Comparison for viscosity solutions of infinity-fractional diffusion
AP · AIM Open Applied Problems · comparison principles · infinity fractional Laplacian · viscosity solutions
OP-00801 Solution claimed
Integral optimal flat-norm decompositions in codimension one
DG · AIM Open Applied Problems · flat norm · integral currents
OP-00802 Solution claimed
Intercritical norm inflation for the dispersion-managed Schrödinger equation
AP · AIM Open Applied Problems · dispersion management · nonlinear Schrödinger equations · norm inflation
OP-00803 Solution claimed
Global smooth propagation for a laser envelope coupled to ionization
AP · AIM Open Applied Problems · laser filamentation · nonlinear Schrödinger equations
OP-00804 Solution claimed
Exponential excursion tails for topology-preserving Ising disks
PR · AIM Open Applied Problems · rare events · self-avoiding polygons · topology-preserving dynamics
OP-00805 Solution claimed
An algebraic vanishing-noise rate for kinetic mean-field games
AP · AIM Open Applied Problems · kinetic mean-field games · vanishing viscosity · variational methods
OP-00806 Solution claimed
Uniform convergence of value functions in local mean-field games
AP · AIM Open Applied Problems · Hamilton–Jacobi equations · mean-field games · vanishing viscosity
OP-00807 Solution claimed
Zero in the upper-Laplacian spectrum of low-degree simplicial complexes
SP · AIM Open Applied Problems · branching random walks · simplicial complexes · upper Laplacian
OP-00808 Solution claimed
Asymmetry at the Macbeath point of a convex body
MG · AIM Open Applied Problems · centers of convex bodies · convex bodies
OP-00809 Solution claimed
Mass conservation for fractional porous-medium flow on noncompact manifolds
AP · AIM Open Applied Problems · fractional porous medium equations · mass conservation · Riemannian manifolds
OP-00810 Solution claimed
Point-source solutions of fractional porous-medium diffusion on manifolds
AP · AIM Open Applied Problems · fractional porous medium equations · fundamental solutions · Riemannian manifolds
OP-00811 Solution claimed
Topological complexity in the homogeneous medial regime for all sample sizes
AT · AIM Open Applied Problems · random simplicial complexes · topological complexity
OP-00812 Solution claimed
Minimal persistence grids versus homological Morse lower bounds
AT · AIM Open Applied Problems · multigraded Betti numbers · multiparameter persistent homology
OP-00813 Solution claimed
A finite-integrability ABP estimate for general nonlocal Pucci operators
AP · AIM Open Applied Problems · Aleksandrov–Bakelman–Pucci estimates · integro-differential equations · Pucci extremal operators
OP-00814 Solution claimed
Odd Euler characteristic for flag-no-square four-manifolds
GT · AIM Open Applied Problems · Euler characteristic · flag-no-square triangulations · four-manifolds
OP-00815 Solution claimed
Can one-dimensional entropy-dissipating systems have two bounded solutions?
AP · AIM Open Applied Problems · entropy solutions · hyperbolic conservation laws
OP-00816 Solution claimed
Coarse Hilbert embeddings of persistence diagrams
MG · AIM Open Applied Problems · coarse embeddings · persistence diagrams · Wasserstein distance
OP-00817 Solution claimed
Betti numbers of a persistence fiber with no finite bars
AT · AIM Open Applied Problems · fibers of the persistence map · persistent homology
OP-00818 Solution claimed
Sharp weak integrability of planar Monge–Ampère Hessians
AP · AIM Open Applied Problems · Monge–Ampère equation · quasiconformal maps · Sobolev regularity
OP-00819 Solution claimed
Location of the most isolated point in a random polyhedral sample
PR · AIM Open Applied Problems · convex polyhedra · nearest-neighbour distances · random geometric graphs
OP-00820 Solution claimed
Singular-set dimension of polyhedral partial-transport free boundaries
AP · AIM Open Applied Problems · free boundaries · Monge–Ampère obstacle problems · optimal partial transport
OP-00821 Solution claimed
Regularity of transport interfaces for nonconvex polyhedral targets
AP · AIM Open Applied Problems · Brenier maps · optimal transport · singular sets
OP-00822 Solution claimed
Connectivity when the last isolated point disappears in a polytope
PR · AIM Open Applied Problems · connectivity threshold · convex polytopes · random geometric graphs
OP-00823 Solution claimed
Maximal TC weight from positive homological norm
AT · AIM Open Applied Problems · simplicial volume · topological complexity
OP-00824 Solution claimed
Limiting Betti-number distributions in preferential-attachment networks
PR · AIM Open Applied Problems · Betti numbers · clique complexes · preferential attachment
OP-00825 Solution claimed
Concentric-ball optimality for thermal insulation with radiative heat transfer
AP · AIM Open Applied Problems · radiative heat transfer · shape optimization · thermal insulation
OP-00826 Solution claimed
Coboundary expansion of random balanced Cayley complexes
CO · AIM Open Applied Problems · Cayley complexes · coboundary expansion · random simplicial complexes
OP-00827 Solution claimed
Central limit theorem for the first path Betti number
PR · AIM Open Applied Problems · central limit theorems · path homology · random directed graphs
OP-00828 Solution claimed
Vanishing threshold for first path homology of a random digraph
AT · AIM Open Applied Problems · path homology · random directed graphs
OP-00829 Solution claimed
Uniqueness of positive reaction–diffusion equilibria outside two obstacles
AP · AIM Open Applied Problems · exterior domains · monostable reactions · reaction–diffusion equations
OP-00830 Solution claimed
A linear threshold for extracting a segment grid
CO · AIM Open Applied Problems · geometric thickness · segment arrangements
OP-00831 Solution claimed
Nill's facet bound for reflexive lattice polytopes
CO · AIM Open Applied Problems · facet numbers · lattice polytopes · reflexive polytopes
OP-00832 Solution claimed
Injectivity of the Rips shadow map on fundamental groups
AT · AIM Open Applied Problems · fundamental group · Vietoris–Rips complexes
OP-00833 Solution claimed
Uniqueness of positive harmonic profiles for singular stable operators in cones
AP · AIM Open Applied Problems · nonlocal elliptic equations · positive solutions in cones · stable operators
OP-00834 Solution claimed
Spanning triangulated spheres with holes in surface triangulations
CO · AIM Open Applied Problems · spanning subgraphs · surface triangulations · triangulated spheres with holes
OP-00835 Solution claimed
The first Rips homotopy transition for higher-dimensional spheres
AT · AIM Open Applied Problems · homotopy types · spheres · Vietoris–Rips complexes
OP-00836 Solution claimed
Extinction at the critical Dirichlet eigenvalue for strong-KPP reactions
AP · AIM Open Applied Problems · generalized principal eigenvalue · reaction–diffusion equations
OP-00837 Solution claimed
Uniqueness of strong-KPP equilibria on general unbounded domains
AP · AIM Open Applied Problems · reaction–diffusion equations · strong-KPP reactions
OP-00838 Solution claimed
The local limit of superlinear multispecies nonlocal diffusion
AP · AIM Open Applied Problems · cross-diffusion systems · nonlocal diffusion · Shigesada–Kawasaki–Teramoto model
OP-00839 Solution claimed
Homotopy type of torus-grid Rips complexes at half the diameter
AT · AIM Open Applied Problems · homotopy types · torus grids · Vietoris–Rips complexes
OP-00840 Solution claimed
Homology at the second transition of torus-grid Rips complexes
AT · AIM Open Applied Problems · integral homology · torus grids · Vietoris–Rips complexes
OP-00841 Solution claimed
A universal quantitative error bound for small-BV hyperbolic flows
AP · AIM Open Applied Problems · a posteriori error estimates · hyperbolic conservation laws
OP-00842 Open
A nonlinear Weyl lemma at the minimal p-harmonic integrability threshold
AP · AIM Open Applied Problems · p-Laplace equation · very weak solutions
OP-00843 Open
Six-point persistence on the Euclidean two-sphere
MG · AIM Open Applied Problems · persistence sets · two-sphere · Vietoris–Rips persistence
OP-00844 Open
Uniqueness of a hemispheric saddle profile on a magnetic sphere
AP · AIM Open Applied Problems · micromagnetics · spherical ferromagnets
OP-00845 Solution claimed
Quadratic-growth rigidity for the complex Monge–Ampère equation
AP · AIM Open Applied Problems · complex Monge–Ampère equations · Liouville theorems
OP-00846 Solution claimed
The minimum vertex number of a triangulation of real projective 5-space
CO · AIM Open Applied Problems · real projective spaces · triangulated manifolds · vertex-minimal triangulations
OP-00847 Open
Bounded geometric thickness for unions of two forests
CO · AIM Open Applied Problems · arboricity · geometric thickness
OP-00848 Open
Compact orbit covers of aspherical manifolds
GT · AIM Open Applied Problems · aspherical manifolds · universal covers
OP-00849 Open
Uniqueness of the Brownian coagulation similarity profile
AP · AIM Open Applied Problems · coagulation equations · self-similar solutions · Smoluchowski's equation
OP-00850 Open
A closed Lagrangian Euler trajectory on a surface of higher genus
AP · AIM Open Applied Problems · closed geodesics · diffeomorphism groups · Euler equations
OP-00851 Open
Bounded weakening for constrained invertibility
CO · AIM Open Applied Problems · constrained invertibility problems · interleaving distance · multiparameter persistence
OP-00852 Open
A sharp differing-edge bound for convex plane-tree flips
CO · AIM Open Applied Problems · flip graphs · non-crossing spanning trees
OP-00853 Open
The happy-edge conjecture for convex plane spanning trees
CO · AIM Open Applied Problems · flip graphs · non-crossing spanning trees
OP-00854 Open
Counting cospherical tuples in lattice cubes
CO · AIM Open Applied Problems · cospherical points · incidence geometry · lattice points
OP-00855 Open
Continuous harmonic extension of every degree-zero sphere boundary map
AP · AIM Open Applied Problems · boundary value problems · harmonic maps
OP-00856 Open
Concentration of eikonal entropy production on jump curves
AP · AIM Open Applied Problems · Aviles–Giga functionals · eikonal equations · entropy productions
OP-00857 Open
Approximation preserving a compressible elastic energy
AP · AIM Open Applied Problems · diffeomorphic approximation · nonlinear elasticity · Sobolev homeomorphisms
OP-00858 Open
Radial classification of higher-degree entire planar Ginzburg–Landau vortices
AP · AIM Open Applied Problems · Ginzburg–Landau equation · radial symmetry · vortices
OP-00859 Open
Polynomial growth of every entire minimal graph
AP · AIM Open Applied Problems · Bernstein theorems · minimal graphs
OP-00860 Open
Surjectivity of the two-dimensional Euler endpoint map
AP · AIM Open Applied Problems · diffeomorphism groups · Euler equations · exponential maps
OP-00861 Open
Sustained double-exponential gradient growth on the Euler torus
AP · AIM Open Applied Problems · Euler equations · small-scale creation · vorticity gradients
OP-00862 Open
Sharp vertex bounds for generalized triangulations in even dimensions
GT · AIM Open Applied Problems · face numbers · triangulated manifolds
OP-00863 Open
Steady planar flow around an obstacle at arbitrary Reynolds number
AP · AIM Open Applied Problems · exterior domains · flows past obstacles · stationary Navier–Stokes equations
OP-00864 Open
A strict gap between face and cycle percolation thresholds
PR · AIM Open Applied Problems · continuum percolation · random simplicial complexes
OP-00865 Open
The maximal heat-transfer exponent at finite Prandtl number
AP · AIM Open Applied Problems · Boussinesq equations · Nusselt numbers · Rayleigh–Bénard convection
OP-00866 Open
Best convex shape for insulation of fixed thickness and perimeter
AP · AIM Open Applied Problems · convex sets · shape optimization · thermal insulation
OP-00867 Open
A sharp Betti-number bound for 4-manifold triangulation complexity
GT · 4-manifolds · AIM Open Applied Problems · generalised triangulations · triangulation complexity
OP-00868 Open
Transversal ratio approaching one for simplicial four-polytopes
CO · AIM Open Applied Problems · hypergraph transversals · simplicial polytopes · weak colorings
OP-00869 Open
Three or four layers for 2-degenerate graphs
CO · AIM Open Applied Problems · degenerate graphs · geometric thickness
OP-00870 Open
Arbitrarily large integer-distance sets in general position
MG · AIM Open Applied Problems · Erdős problems · general position · integer distance sets
OP-00871 Open
Existence of a nonaffine polynomial minimal graph
AP · AIM Open Applied Problems · minimal graphs · polynomial solutions
OP-00872 Open
Reconstructing simplicial spheres from facet adjacency
CO · AIM Open Applied Problems · facet-ridge graphs · polytope reconstruction · simplicial spheres
OP-00873 Open
Global classical solutions of the spatially inhomogeneous Landau–Coulomb equation
AP · AIM Open Applied Problems · global classical solutions · kinetic equations · Landau equation
OP-00874 Open
Anomalous viscous dissipation with fixed large-scale forcing
AP · AIM Open Applied Problems · anomalous dissipation · Navier–Stokes equations · turbulence
OP-00875 Open
Stationarity of Lipschitz weak solutions of the minimal-surface system
AP · AIM Open Applied Problems · minimal graphs · weak solutions
OP-00876 Open
Tagged-particle thermalization with an interacting background
AP · AIM Open Applied Problems · Lenard–Balescu equation · mean-field limits · tagged particles
OP-00877 Open
Hardness of minimum-dilation triangulation
MG · AIM Open Applied Problems · geometric spanners · NP-hardness · triangulations
OP-00878 Open
An inertial manifold for the two-dimensional Navier–Stokes flow
AP · AIM Open Applied Problems · global attractors · inertial manifolds · Navier–Stokes equations
OP-00879 Open
Multiplicity one at planar network singularities
AP · AIM Open Applied Problems · curvature flows · planar networks · self-similar shrinkers
OP-00880 Open
Exact diameter of the leaf-slide graph on labelled trees
CO · AIM Open Applied Problems · labelled trees · network realignment complexes · reconfiguration graphs
OP-00881 Open
Uniqueness of the limiting shape at a network singularity
AP · AIM Open Applied Problems · blow-up limits · curvature flows · planar networks
OP-00882 Open
The nonlinear Landau limit of weakly interacting particles
AP · AIM Open Applied Problems · Landau equation · particle systems · weak-coupling limits
OP-00883 Open
Motion-planning complexity of symmetric products of non-orientable surfaces
AT · AIM Open Applied Problems · non-orientable surfaces · symmetric products · topological complexity
OP-00884 Open
Energy conservation at the exact Onsager Hölder exponent
AP · AIM Open Applied Problems · energy conservation · Euler equations · Onsager's conjecture
OP-00885 Open
Wedge-of-spheres structure of path-product matching complexes
CO · AIM Open Applied Problems · categorical products of graphs · matching complexes · wedges of spheres
OP-00886 Open
Improving the exponential lower bound for peeling sequences
CO · AIM Open Applied Problems · convex hulls · peeling sequences · point sets
OP-00887 Open
Planar Rips complexes as wedges of spheres
AT · AIM Open Applied Problems · homotopy types · Vietoris–Rips complexes · wedges of spheres
OP-00888 Open
Connectivity of plane spanning-path reconfiguration
CO · AIM Open Applied Problems · flip graphs · plane spanning paths · reconfiguration
OP-00889 Open
Polynomial anisotropic minimal graphs in dimensions four and five
AP · AIM Open Applied Problems · anisotropic minimal hypersurfaces · Bernstein theorems
OP-00890 Open
Polynomial-size convex difference decompositions
MG · AIM Open Applied Problems · DC decompositions · piecewise linear functions · polyhedral complexes
OP-00891 Open
Polynomial bounds for the graph diameter of polytopes
CO · AIM Open Applied Problems · convex polytopes · graph diameter · Hirsch conjecture
OP-00892 Open
Maximal motion-planning complexity from positive simplicial volume
AT · AIM Open Applied Problems · aspherical manifolds · simplicial volume · topological complexity
OP-00893 Open
Exact motion-planning complexity of real projective spaces
AT · AIM Open Applied Problems · immersions · real projective spaces · topological complexity
OP-00894 Open
The sharp radius in quantitative Steinitz selection
MG · AIM Open Applied Problems · convex hulls · quantitative Steinitz theorems · sparse approximation
OP-00895 Open
A limiting law for maximal persistence in random clique complexes
PR · AIM Open Applied Problems · persistent homology · random clique complexes
OP-00896 Open
Uniqueness of bounded semigeostrophic potential vorticity
AP · AIM Open Applied Problems · optimal transport · semigeostrophic equations · weak solutions
OP-00897 Open
Global smooth evolution of small semigeostrophic perturbations
AP · AIM Open Applied Problems · global smooth solutions · Monge–Ampère equations · semigeostrophic equations
OP-00898 Open
Sierksma's lower bound for Tverberg partitions
MG · AIM Open Applied Problems · Sierksma's conjecture · Tverberg partitions
OP-00899 Open
Eventual classification of simplicial line arrangements
CO · AIM Open Applied Problems · line arrangements · simplicial arrangements
OP-00900 Open
Monotonicity of connectivity in spherical Čech filtrations
AT · AIM Open Applied Problems · Čech complexes · homotopy connectivity · spheres
OP-00901 Open
Finite homotopy models for spherical Čech complexes
AT · AIM Open Applied Problems · Čech complexes · homotopy types · spheres
OP-00902 Open
Monotonicity of connectivity in spherical Rips filtrations
AT · AIM Open Applied Problems · homotopy connectivity · spheres · Vietoris–Rips complexes
OP-00903 Open
Finite homotopy models for spherical Rips complexes
AT · AIM Open Applied Problems · homotopy types · spheres · Vietoris–Rips complexes
OP-00904 Open
A stationary isotropic gas of freely moving non-colliding disks
PR · AIM Open Applied Problems · hard-disk systems · stationary point processes
OP-00905 Open
The finite-Dirichlet Liouville problem for steady three-dimensional flow
AP · AIM Open Applied Problems · Liouville theorems · stationary Navier–Stokes equations
OP-00906 Open
Convex realizations of spherical subword complexes
CO · AIM Open Applied Problems · Coxeter groups · simplicial polytopes · subword complexes
OP-00907 Open
The full set of zero-energy cubic-to-tetragonal strains
AP · AIM Open Applied Problems · martensitic phase transformations · quasiconvex hulls
OP-00908 Open
Unbounded weak chromatic number for geometric tetrahedral complexes
CO · AIM Open Applied Problems · geometric hypergraphs · simplicial complexes · weak colorings
OP-00909 Open
Sharp enstrophy-limited heat transport in two dimensions
AP · advection–diffusion equations · AIM Open Applied Problems · branching flows · heat transport
OP-00910 Open
Uniqueness of 277-point two-distance sets in dimension 23
MG · AIM Open Applied Problems · distance geometry · two-distance sets
OP-00911 Open
A 325-point two-distance set in dimension 24
MG · AIM Open Applied Problems · distance geometry · two-distance sets
OP-00912 Open
The unregularized Coulomb mean-field limit
AP · AIM Open Applied Problems · Coulomb interactions · mean-field limits · Vlasov–Poisson equation
OP-00913 Open
Unimodal connectivity by 2–3 and 3–2 Pachner moves
GT · 3-manifold triangulations · AIM Open Applied Problems · Pachner moves · unimodal sequences
OP-00914 Open
Monotonicity of unordered graph motion-planning complexity
AT · AIM Open Applied Problems · configuration spaces · graph braid groups · topological complexity
OP-00915 Open
The Euler vortex-filament limit for a general moving curve
AP · AIM Open Applied Problems · binormal curvature flow · Euler equations · vortex filaments
OP-00916 Open
Uniqueness of the zero-average dispersion-managed soliton
AP · AIM Open Applied Problems · dispersion management · ground states · nonlinear Schrödinger equations
OP-00917 Open
Injectivity radius of the canonical Stiefel manifold
DG · AIM Open Applied Problems · conjugate points · injectivity radius · Stiefel manifold
OP-00918 Open
The Hardy–Littlewood prime k-tuples conjecture
NT · Hardy–Littlewood conjectures · prime constellations · prime k-tuples · singular series
OP-00919 Open
The Hardy–Littlewood asymptotic formula for Goldbach representations
NT · additive prime number theory · Goldbach's conjecture · Hardy–Littlewood conjectures · singular series
OP-00920 Open
The Hardy–Littlewood asymptotic formula for prime pairs with a given difference
NT · Hardy–Littlewood conjectures · prime gaps · singular series · twin primes
OP-00921 Open
Representations n = ap + bp′ by two primes with fixed coefficients
NT · additive prime number theory · Goldbach's conjecture · Hardy–Littlewood conjectures · singular series
OP-00922 Open
Prime solutions of the linear equation ap′ − bp = k
NT · Hardy–Littlewood conjectures · linear equations in primes · prime pairs · singular series
OP-00923 Open
The Hardy–Littlewood asymptotic formula for primes of the form m² + 1
NT · Hardy–Littlewood conjectures · Landau's problems · primes represented by polynomials
OP-00924 Open
Primes represented by a quadratic polynomial am² + bm + c
NT · Bunyakovsky conjecture · Hardy–Littlewood conjectures · primes represented by polynomials
OP-00925 Open
Representations n = am² + bm + p by a quadratic and a prime
NT · additive prime number theory · Hardy–Littlewood conjectures · quadratic polynomials
OP-00926 Open
Every large non-square is a prime plus a square
NT · additive prime number theory · Hardy–Littlewood conjectures · sums of a prime and a square
OP-00927 Open
Every large odd number is a prime plus twice a square
NT · additive prime number theory · Goldbach's other conjecture · Hardy–Littlewood conjectures
OP-00928 Open
Primes of the form m³ + k
NT · cubic residues · Hardy–Littlewood conjectures · primes represented by polynomials
OP-00929 Open
Every large non-cube is a prime plus a cube
NT · additive prime number theory · cubic residues · Hardy–Littlewood conjectures
OP-00930 Open
Primes of the form l³ + m³ + k
NT · cubic residues · Hardy–Littlewood conjectures · primes represented by polynomials · sums of cubes
OP-00931 Open
Asymptotic count of primes that are sums of three positive cubes
NT · cubic residues · Hardy–Littlewood conjectures · primes represented by polynomials · sums of cubes
OP-00932 Open
Prime pairs m² + 1, m² + 3
NT · Hardy–Littlewood conjectures · prime pairs · primes represented by polynomials
OP-00933 Open
Positive density of Ulam's sequence
NT · additive number theory · Ulam sequence · unique representations
OP-00934 Open
A Lipschitz function on the natural numbers whose graph has no three-term progression
CO · additive squares · arithmetic progressions · combinatorics on words
OP-00935 Open
Naïve corners in products of finite groups
CO · corners · density theorems · finite groups · quasirandom groups
OP-00936 Open
Rado's boundedness conjecture
CO · colourings · linear equations · partition regularity · Rado's theorem
OP-00937 Open
A long gap in a dilate of a square-root-sized set modulo a prime
NT · cyclic groups of prime order · dilates · gaps · polynomial method
OP-00938 Open
Additive bases of cyclic groups of nearly optimal size
NT · additive bases · cyclic groups · Sidon sets · sumsets
OP-00939 Open
Covering a cyclic group by few translates of a random set
CO · covering · cyclic groups of prime order · random sets · translates
OP-00940 Open
Density of linear covering codes of large radius
CO · coding theory · covering codes · Hamming balls · linear codes
OP-00941 Open
Residue classes modulo primes slightly above the square root
NT · Kakeya problem · large sieve · residue classes · sieve theory
OP-00942 Open
Covering every integer up to N ten times by one residue class per prime
NT · covering systems · Erdős problems · residue classes · sieve theory
OP-00943 Open
Cosets in A + A for sets with a small additive complement
CO · additive combinatorics · additive complements · Bogolyubov's lemma · finite field model · sumsets
OP-00944 Open
A composite number in a sumset below the square-root threshold
NT · inverse Goldbach problem · large sieve · primes · sumsets
OP-00945 Open
Every integer as a sum of two very smooth numbers
NT · binary additive problems · Erdős problems · friable integers · smooth numbers
OP-00946 Open
Sumsets of sets of squares grow by a power
NT · Rudin's conjecture · squares · sumsets · Λ(p) sets
OP-00947 Open
Small sets whose sumset contains the first n squares
NT · additive bases · Erdős problems · squares · sumsets
OP-00948 Open
Primes p for which p − 2 has an odd number of prime factors
NT · Liouville function · parity problem · shifted primes · twin primes
OP-00949 Open
A sum of two squares just below every large number
NT · gaps · Littlewood's problems · short intervals · sums of two squares
OP-00950 Open
Arcs in the plane over a prime field lie mostly on a cubic curve
CO · algebraic curves · arcs · finite geometry · no-three-in-line
OP-00951 Open
Many collinear triples force a cubic curve with many points
CO · collinear triples · cubic curves · incidence geometry · orchard problem
OP-00952 Open
Many collinear four-point sets force five points on a line
CO · collinear points · Erdős problems · incidence geometry · rich lines
OP-00953 Open
The Kupitz–Perles balanced line conjecture
CO · balanced lines · discrete geometry · halving lines · lines through point sets
OP-00954 Open
Weak nets of linear size for axis-parallel rectangles
CO · axis-parallel rectangles · discrepancy theory · discrete geometry · weak epsilon-nets
OP-00955 Open
Random generators of the alternating group give fast mixing
GR · alternating groups · Cayley graphs · expanders · mixing time · random walks on groups
OP-00956 Open
Carbery's rectangle problem
CA · axis-parallel rectangles · harmonic analysis · measure theory · sublevel sets
OP-00957 Open
A dilate with no short interval holding many points
NT · dilates · discrepancy · uniform distribution modulo one
OP-00958 Open
Large sets of pairwise comparable triples
CO · comparability · Delsarte bound · extremal combinatorics · independent sets · tripod packing
OP-00959 Open
The dichotomy problem for Sidon sets and sets of analyticity
CA · commutative harmonic analysis · Fourier algebra · functions operating on Fourier coefficients · sets of analyticity · Sidon sets
OP-00960 Open
Indices of irreducible subfactors of the hyperfinite II₁ factor
OA · hyperfinite II₁ factor · Jones index · Peterson's operator algebra problems · subfactors
OP-00961 Open
Does every nonamenable II₁ factor contain the free group factor L(F₂)?
OA · amenability · free group factors · II₁ factors · Peterson's operator algebra problems
OP-00962 Open
The Stone–Weierstrass problem for C*-algebras
OA · C*-algebras · Peterson's operator algebra problems · pure states · Stone–Weierstrass theorem
OP-00963 Open
Are the radial and generator masas of L(F₂) conjugate by an automorphism?
OA · free group factors · maximal abelian subalgebras · Peterson's operator algebra problems · radial masa
OP-00964 Open
Do reduced group C*-algebras remember torsion-free groups?
OA · C*-superrigidity · Peterson's operator algebra problems · reduced group C*-algebras · torsion-free groups
OP-00965 Open
Tensor factors of McDuff II₁ factors
OA · central sequences · McDuff factors · Peterson's operator algebra problems · tensor products
OP-00966 Open
Uniqueness of McDuff decompositions up to amplification
OA · amplifications · McDuff decomposition · McDuff factors · Peterson's operator algebra problems
OP-00967 Open
Tensor products of maximal injective subalgebras
OA · II₁ factors · maximal injective subalgebras · Peterson's operator algebra problems · tensor products
OP-00968 Open
Kadison's problem on finitely generated *-algebras of operators with finite spectra
OA · *-algebras · finite spectrum · operator algebras · Peterson's operator algebra problems
OP-00969 Open
Cocycle superrigidity of Bernoulli actions of groups with vanishing first ℓ²-Betti number
OA · Bernoulli actions · cocycle superrigidity · ℓ²-Betti numbers · Peterson's operator algebra problems
OP-00970 Open
Trivial fundamental group for Bernoulli crossed products
OA · Bernoulli actions · fundamental group of II₁ factors · ℓ²-Betti numbers · Peterson's operator algebra problems
OP-00971 Open
Popa's factorial commutant embedding problem
OA · hyperfinite II₁ factor · Peterson's operator algebra problems · relative commutants · ultrapowers
OP-00972 Open
Isomorphism of matrix ultraproducts under the continuum hypothesis
OA · continuous model theory · continuum hypothesis · matrix algebras · Peterson's operator algebra problems · ultraproducts
OP-00973 Open
Cost of a group and its first ℓ²-Betti number
GR · cost · ℓ²-Betti numbers · measured group theory · Peterson's operator algebra problems
OP-00974 Open
Nonamenable subfactors of the free group factor L(F₂)
OA · free group factors · interpolated free group factors · Peterson's operator algebra problems · subfactors
OP-00975 Open
A discrete copy of the free group in the unitary group of the hyperfinite II₁ factor
OA · discrete subgroups · free groups · hyperfinite II₁ factor · Peterson's operator algebra problems · unitary groups
OP-00976 Open
Unitary representations of higher-rank lattices in the hyperfinite II₁ factor
OA · hyperfinite II₁ factor · lattices in Lie groups · Peterson's operator algebra problems · rigidity · unitary representations
OP-00977 Open
Unique Cartan subalgebra for Bernoulli crossed products
OA · Bernoulli actions · Cartan subalgebras · group measure space construction · Peterson's operator algebra problems
OP-00978 Open
Unique Cartan subalgebra for SLₙ(ℤ) acting on the n-torus
OA · Cartan subalgebras · group measure space construction · Peterson's operator algebra problems · toral automorphisms
OP-00979 Open
Unique Cartan subalgebras for groups with a nonzero ℓ²-Betti number
OA · Cartan subalgebras · C-rigidity · ℓ²-Betti numbers · Peterson's operator algebra problems
OP-00980 Open
Are locally reflexive C*-algebras exact?
OA · C*-algebras · exactness · local reflexivity · Peterson's operator algebra problems