clopen.solutions

Open problems

980 registered problems.

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