clopen.solutions

Open problems

980 registered problems.

OP-00867 Open
A sharp Betti-number bound for 4-manifold triangulation complexity
GT · 4-manifolds · AIM Open Applied Problems · generalised triangulations · triangulation complexity
OP-00868 Open
Transversal ratio approaching one for simplicial four-polytopes
CO · AIM Open Applied Problems · hypergraph transversals · simplicial polytopes · weak colorings
OP-00869 Open
Three or four layers for 2-degenerate graphs
CO · AIM Open Applied Problems · degenerate graphs · geometric thickness
OP-00870 Open
Arbitrarily large integer-distance sets in general position
MG · AIM Open Applied Problems · Erdős problems · general position · integer distance sets
OP-00871 Open
Existence of a nonaffine polynomial minimal graph
AP · AIM Open Applied Problems · minimal graphs · polynomial solutions
OP-00872 Open
Reconstructing simplicial spheres from facet adjacency
CO · AIM Open Applied Problems · facet-ridge graphs · polytope reconstruction · simplicial spheres
OP-00873 Open
Global classical solutions of the spatially inhomogeneous Landau–Coulomb equation
AP · AIM Open Applied Problems · global classical solutions · kinetic equations · Landau equation
OP-00874 Open
Anomalous viscous dissipation with fixed large-scale forcing
AP · AIM Open Applied Problems · anomalous dissipation · Navier–Stokes equations · turbulence
OP-00875 Open
Stationarity of Lipschitz weak solutions of the minimal-surface system
AP · AIM Open Applied Problems · minimal graphs · weak solutions
OP-00876 Open
Tagged-particle thermalization with an interacting background
AP · AIM Open Applied Problems · Lenard–Balescu equation · mean-field limits · tagged particles
OP-00877 Open
Hardness of minimum-dilation triangulation
MG · AIM Open Applied Problems · geometric spanners · NP-hardness · triangulations
OP-00878 Open
An inertial manifold for the two-dimensional Navier–Stokes flow
AP · AIM Open Applied Problems · global attractors · inertial manifolds · Navier–Stokes equations
OP-00879 Open
Multiplicity one at planar network singularities
AP · AIM Open Applied Problems · curvature flows · planar networks · self-similar shrinkers
OP-00880 Open
Exact diameter of the leaf-slide graph on labelled trees
CO · AIM Open Applied Problems · labelled trees · network realignment complexes · reconfiguration graphs
OP-00881 Open
Uniqueness of the limiting shape at a network singularity
AP · AIM Open Applied Problems · blow-up limits · curvature flows · planar networks
OP-00882 Open
The nonlinear Landau limit of weakly interacting particles
AP · AIM Open Applied Problems · Landau equation · particle systems · weak-coupling limits
OP-00883 Open
Motion-planning complexity of symmetric products of non-orientable surfaces
AT · AIM Open Applied Problems · non-orientable surfaces · symmetric products · topological complexity
OP-00884 Open
Energy conservation at the exact Onsager Hölder exponent
AP · AIM Open Applied Problems · energy conservation · Euler equations · Onsager's conjecture
OP-00885 Open
Wedge-of-spheres structure of path-product matching complexes
CO · AIM Open Applied Problems · categorical products of graphs · matching complexes · wedges of spheres
OP-00886 Open
Improving the exponential lower bound for peeling sequences
CO · AIM Open Applied Problems · convex hulls · peeling sequences · point sets
OP-00887 Open
Planar Rips complexes as wedges of spheres
AT · AIM Open Applied Problems · homotopy types · Vietoris–Rips complexes · wedges of spheres
OP-00888 Open
Connectivity of plane spanning-path reconfiguration
CO · AIM Open Applied Problems · flip graphs · plane spanning paths · reconfiguration
OP-00889 Open
Polynomial anisotropic minimal graphs in dimensions four and five
AP · AIM Open Applied Problems · anisotropic minimal hypersurfaces · Bernstein theorems
OP-00890 Open
Polynomial-size convex difference decompositions
MG · AIM Open Applied Problems · DC decompositions · piecewise linear functions · polyhedral complexes
OP-00891 Open
Polynomial bounds for the graph diameter of polytopes
CO · AIM Open Applied Problems · convex polytopes · graph diameter · Hirsch conjecture
OP-00892 Open
Maximal motion-planning complexity from positive simplicial volume
AT · AIM Open Applied Problems · aspherical manifolds · simplicial volume · topological complexity
OP-00893 Open
Exact motion-planning complexity of real projective spaces
AT · AIM Open Applied Problems · immersions · real projective spaces · topological complexity
OP-00894 Open
The sharp radius in quantitative Steinitz selection
MG · AIM Open Applied Problems · convex hulls · quantitative Steinitz theorems · sparse approximation
OP-00895 Open
A limiting law for maximal persistence in random clique complexes
PR · AIM Open Applied Problems · persistent homology · random clique complexes
OP-00896 Open
Uniqueness of bounded semigeostrophic potential vorticity
AP · AIM Open Applied Problems · optimal transport · semigeostrophic equations · weak solutions
OP-00897 Open
Global smooth evolution of small semigeostrophic perturbations
AP · AIM Open Applied Problems · global smooth solutions · Monge–Ampère equations · semigeostrophic equations
OP-00898 Open
Sierksma's lower bound for Tverberg partitions
MG · AIM Open Applied Problems · Sierksma's conjecture · Tverberg partitions
OP-00899 Open
Eventual classification of simplicial line arrangements
CO · AIM Open Applied Problems · line arrangements · simplicial arrangements
OP-00900 Open
Monotonicity of connectivity in spherical Čech filtrations
AT · AIM Open Applied Problems · Čech complexes · homotopy connectivity · spheres
OP-00901 Open
Finite homotopy models for spherical Čech complexes
AT · AIM Open Applied Problems · Čech complexes · homotopy types · spheres
OP-00902 Open
Monotonicity of connectivity in spherical Rips filtrations
AT · AIM Open Applied Problems · homotopy connectivity · spheres · Vietoris–Rips complexes
OP-00903 Open
Finite homotopy models for spherical Rips complexes
AT · AIM Open Applied Problems · homotopy types · spheres · Vietoris–Rips complexes
OP-00904 Open
A stationary isotropic gas of freely moving non-colliding disks
PR · AIM Open Applied Problems · hard-disk systems · stationary point processes
OP-00905 Open
The finite-Dirichlet Liouville problem for steady three-dimensional flow
AP · AIM Open Applied Problems · Liouville theorems · stationary Navier–Stokes equations
OP-00906 Open
Convex realizations of spherical subword complexes
CO · AIM Open Applied Problems · Coxeter groups · simplicial polytopes · subword complexes
OP-00907 Open
The full set of zero-energy cubic-to-tetragonal strains
AP · AIM Open Applied Problems · martensitic phase transformations · quasiconvex hulls
OP-00908 Open
Unbounded weak chromatic number for geometric tetrahedral complexes
CO · AIM Open Applied Problems · geometric hypergraphs · simplicial complexes · weak colorings
OP-00909 Open
Sharp enstrophy-limited heat transport in two dimensions
AP · advection–diffusion equations · AIM Open Applied Problems · branching flows · heat transport
OP-00910 Open
Uniqueness of 277-point two-distance sets in dimension 23
MG · AIM Open Applied Problems · distance geometry · two-distance sets
OP-00911 Open
A 325-point two-distance set in dimension 24
MG · AIM Open Applied Problems · distance geometry · two-distance sets
OP-00912 Open
The unregularized Coulomb mean-field limit
AP · AIM Open Applied Problems · Coulomb interactions · mean-field limits · Vlasov–Poisson equation
OP-00913 Open
Unimodal connectivity by 2–3 and 3–2 Pachner moves
GT · 3-manifold triangulations · AIM Open Applied Problems · Pachner moves · unimodal sequences
OP-00914 Open
Monotonicity of unordered graph motion-planning complexity
AT · AIM Open Applied Problems · configuration spaces · graph braid groups · topological complexity
OP-00915 Open
The Euler vortex-filament limit for a general moving curve
AP · AIM Open Applied Problems · binormal curvature flow · Euler equations · vortex filaments
OP-00916 Open
Uniqueness of the zero-average dispersion-managed soliton
AP · AIM Open Applied Problems · dispersion management · ground states · nonlinear Schrödinger equations