Open problems

980 registered problems.

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