clopen.solutions

Open problems

1131 registered problems.

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