Open problems

1131 registered problems.

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