Open problems

1131 registered problems.

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

OP-00767 Solution claimed

Characterizing realizable geodesic scattering data

DG · AIM Open Applied Problems · geometric inverse problems · scattering relation · simple surfaces

OP-00768 Solution claimed

Automorphism-invariant one-dependent colorings of regular trees

PR · AIM Open Applied Problems · finitely dependent processes · proper colorings · regular trees

OP-00769 Solution claimed

The sharp local maneuvering time for a shallow-water tank

OC · AIM Open Applied Problems · local controllability · Saint-Venant equations · water tank

OP-00770 Solution claimed

Sharp characterization of exactly trackable boundary heat fluxes

AP · AIM Open Applied Problems · boundary control · heat equation · tracking controllability

OP-00771 Solution claimed

Sharp local approximation widths for rough elliptic equations

NA · AIM Open Applied Problems · elliptic equations with rough coefficients · Kolmogorov n-widths · multiscale finite element methods

OP-00772 Solution claimed

Boundary observation of a Schrödinger field with slower surface dispersion

OC · AIM Open Applied Problems · dynamic boundary conditions · observability · Schrödinger equation

OP-00773 Solution claimed

Does integration of uniformly derivative-bounded analytic functions suffer the dimensional curse?

NA · AIM Open Applied Problems · curse of dimensionality · information-based complexity · numerical integration

OP-00774 Solution claimed

Sharp asymptotic constant for rational approximation of fractional inverse powers

NA · AIM Open Applied Problems · fractional powers · rational approximation · Stieltjes functions

OP-00775 Solution claimed

Draws in the undirected trapping game on percolation clusters

PR · AIM Open Applied Problems · combinatorial games · site percolation

OP-00776 Solution claimed

Uniqueness of nonnegative heat controls at the minimum time

AP · AIM Open Applied Problems · constrained control · heat equation · minimal control time

OP-00777 Solution claimed

Deciding nonnegativity of unnormalized univariate trace polynomials

AG · AIM Open Applied Problems · decidability · power sums · trace polynomials

OP-00778 Solution claimed

Strong convergence rate of the fractional WIS Euler integrator

NA · AIM Open Applied Problems · fractional Brownian motion · strong convergence · Wick–Itô–Skorohod integral

OP-00779 Solution claimed

Maximal motion-planning complexity of aspherical connected sums

AT · AIM Open Applied Problems · aspherical manifolds · connected sums · topological complexity

OP-00780 Solution claimed

The centre-rank formula for aspherical motion planning

AT · AIM Open Applied Problems · aspherical manifolds · centre of the fundamental group · topological complexity

OP-00781 Solution claimed

Small mod-two area cycles in drawings with bounded pairwise intersections

CO · AIM Open Applied Problems · Heilbronn problems · mod-two cycles · topological graphs

OP-00782 Solution claimed

Positive equilibrium attraction for an irreversible catalytic reaction

AP · AIM Open Applied Problems · chemical reaction networks · convergence to equilibrium · reaction-diffusion systems

OP-00783 Solution claimed

Calderón–Zygmund estimates for general concave nonlocal equations

AP · AIM Open Applied Problems · Bellman equations · fully nonlinear integro-differential equations · Sobolev estimates

OP-00784 Solution claimed

Polynomial decay for KdV with three critical linear modes

AP · AIM Open Applied Problems · critical lengths · decay rates · Korteweg–de Vries equation

OP-00785 Solution claimed

Continuation of the cutoff Boltzmann flow from macroscopic bounds

AP · AIM Open Applied Problems · Boltzmann equation · conditional regularity

OP-00786 Solution claimed

Unconditional uniqueness for entropy-dissipating reaction–diffusion

AP · AIM Open Applied Problems · reaction–diffusion systems · renormalized solutions · uniqueness

OP-00787 Solution claimed

Characterizing discrete sets generated by fixed-parameter extrapolation

MG · AIM Open Applied Problems · aperiodic order · fixed-parameter extrapolation · Pisot numbers

OP-00788 Solution claimed

Relative density of sets generated by fixed-parameter extrapolation

MG · AIM Open Applied Problems · aperiodic order · fixed-parameter extrapolation · relatively dense sets

OP-00789 Solution claimed

An extreme solitary wave for the bidirectional Whitham system

AP · AIM Open Applied Problems · highest waves · solitary waves · Whitham–Boussinesq system

OP-00790 Solution claimed

A bounded number of flat transversals for fat convex sets

MG · AIM Open Applied Problems · fat convex sets · geometric transversals · Helly-type theorems

OP-00791 Solution claimed

The zero center-of-mass diffusion limit for kinetic FENE fluids

AP · AIM Open Applied Problems · dilute polymeric fluids · FENE dumbbell model

OP-00792 Solution claimed

A finite three-ample complex with nontrivial fundamental group

AT · AIM Open Applied Problems · ample simplicial complexes · fundamental group

OP-00793 Solution claimed

Continuity of finite-cluster mass at the onset of Flory gelation

AP · AIM Open Applied Problems · coagulation equations · gelation

OP-00794 Solution claimed

Finite propagation in fourth-order aggregation–diffusion

AP · aggregation-diffusion equations · AIM Open Applied Problems · finite speed of propagation · thin-film equations

OP-00795 Solution claimed

Continuity for degenerate fractional-pressure porous-medium flow

AP · AIM Open Applied Problems · continuity of weak solutions · fractional pressure · porous medium equations

OP-00796 Solution claimed

Optimal obstacle regularity for stable jump kernels with only angular integrability

AP · AIM Open Applied Problems · nonlocal obstacle problems · stable operators

OP-00797 Solution claimed

Counting half-integral polygons with collinear interior lattice points

CO · AIM Open Applied Problems · lattice polygons · rational polygons

OP-00798 Solution claimed

Counting Ehrhart quasipolynomials of half-integral polygons

CO · AIM Open Applied Problems · Ehrhart quasipolynomials · rational polygons

OP-00799 Solution claimed

Ergodicity of higher-dimensional Ising clumps

PR · AIM Open Applied Problems · cubical sets · Markov chains · topology-preserving dynamics

OP-00800 Solution claimed

Comparison for viscosity solutions of infinity-fractional diffusion

AP · AIM Open Applied Problems · comparison principles · infinity fractional Laplacian · viscosity solutions