clopen.solutions

Open problems

980 registered problems.

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