Open problems

AP · AIM Open Applied Problems · coercivity estimates · fractional Sobolev spaces · integro-differential operators

NA · AIM Open Applied Problems · boundary integral equations · Helmholtz equation · Nyström method

AP · AIM Open Applied Problems · Alt–Caffarelli functional · minimizing cones · one-phase free boundary problem

SP · AIM Open Applied Problems · convex domains · hot spots conjecture · Neumann eigenfunctions

PR · AIM Open Applied Problems · deletion channel · sample complexity · trace reconstruction

MP · AIM Open Applied Problems · completely positive maps · entanglement breaking channels · PPT squared conjecture

PR · AIM Open Applied Problems · Onsager–Machlup functionals · product measures · small-ball probabilities

DS · AIM Open Applied Problems · Hilbert's sixteenth problem · limit cycles · quadratic vector fields

DS · AIM Open Applied Problems · chemical reaction networks · mass-action kinetics · persistence

AP · AIM Open Applied Problems · Boltzmann equation · renormalized solutions · uniqueness

SP · AIM Open Applied Problems · convex domains · fundamental gap · Robin Laplacian

AP · AIM Open Applied Problems · Calderón problem · Dirichlet-to-Neumann map · electrical impedance tomography

PR · AIM Open Applied Problems · random walk in random environment · zero–one laws

PR · AIM Open Applied Problems · ballisticity · random walk in random environment

CO · AIM Open Applied Problems · graph homomorphisms · Sidorenko's conjecture

MG · AIM Open Applied Problems · convex bodies · isotropic constant · slicing problem

AP · AIM Open Applied Problems · Calderón problem · Dirichlet-to-Neumann map · Riemannian manifolds

CA · AIM Open Applied Problems · extension operator · Fourier restriction · sphere

PR · AIM Open Applied Problems · conformal invariance · critical percolation · crossing probabilities

DS · AIM Open Applied Problems · Lyapunov exponents · metric entropy · standard map

AP · AIM Open Applied Problems · inverse problems · Lamé parameters · linear elasticity

CA · AIM Open Applied Problems · directional Hilbert transform · Lipschitz vector fields · singular integrals

SP · AIM Open Applied Problems · nodal sets · Steklov eigenfunctions · Yau's conjecture

SP · AIM Open Applied Problems · interior decay · Steklov eigenfunctions

PR · AIM Open Applied Problems · first-passage percolation · limit shapes

CO · AIM Open Applied Problems · edge connectivity · spanning trees · thin trees

MP · AIM Open Applied Problems · Bose-Einstein condensation · dilute Bose gases · thermodynamic limit

OC · AIM Open Applied Problems · computational complexity · makespan · precedence-constrained scheduling

CA · AIM Open Applied Problems · multilinear singular integrals · triangular Hilbert transform

MG · AIM Open Applied Problems · Gaussian energy · triangular lattice · universal optimality

MP · AIM Open Applied Problems · area law · entanglement entropy · gapped ground states

SP · AIM Open Applied Problems · Coulomb systems · ionization conjecture · many-body Schrödinger operators

CO · AIM Open Applied Problems · constraint satisfaction · hardness of approximation · Unique Games Conjecture

NA · AIM Open Applied Problems · Aronson–Bénilan estimate · porous medium equation · upwind schemes

AT · AIM Open Applied Problems · persistent homology · verbose barcodes · Vietoris–Rips complexes

DG · AIM Open Applied Problems · injectivity domains · Ma–Trudinger–Wang condition · optimal transport

AP · AIM Open Applied Problems · global classical solutions · kinetic theory · Vlasov–Maxwell system

SP · AIM Open Applied Problems · Laplace eigenfunctions · nodal sets · Yau's conjecture

MG · AIM Open Applied Problems · Gromov–Wasserstein distance · measure networks · path connectedness

OC · AIM Open Applied Problems · analytic control systems · reachable sets · small-time local controllability

AP · AIM Open Applied Problems · Bourgain–Brezis estimates · divergence equation · fractional Sobolev spaces

AP · AIM Open Applied Problems · Burgers equation · null controllability · vanishing viscosity

DS · AIM Open Applied Problems · carrying simplex · competitive maps · invariant manifolds

FA · AIM Open Applied Problems · Dirichlet-to-Neumann operator · holomorphic semigroups · Lipschitz domains

AP · AIM Open Applied Problems · Fisher information · Fokker–Planck equation · relative entropy

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

RA · AIM Open Applied Problems · free Lie algebras · Poisson brackets · splitting methods

PR · AIM Open Applied Problems · finitely dependent processes · proper colorings · star graphs

NA · AIM Open Applied Problems · boundary element methods · fractal screens · single-layer operator

NA · AIM Open Applied Problems · finite elements · Freudenthal meshes · Stokes complex