clopen.solutions

Open problems

1131 registered problems.

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
OP-00917 Open
Injectivity radius of the canonical Stiefel manifold
DG · AIM Open Applied Problems · conjugate points · injectivity radius · Stiefel manifold
OP-00918 Open
The Hardy–Littlewood prime k-tuples conjecture
NT · Hardy–Littlewood conjectures · prime constellations · prime k-tuples · singular series
OP-00919 Open
The Hardy–Littlewood asymptotic formula for Goldbach representations
NT · additive prime number theory · Goldbach's conjecture · Hardy–Littlewood conjectures · singular series
OP-00920 Open
The Hardy–Littlewood asymptotic formula for prime pairs with a given difference
NT · Hardy–Littlewood conjectures · prime gaps · singular series · twin primes
OP-00921 Open
Representations n = ap + bp′ by two primes with fixed coefficients
NT · additive prime number theory · Goldbach's conjecture · Hardy–Littlewood conjectures · singular series
OP-00922 Open
Prime solutions of the linear equation ap′ − bp = k
NT · Hardy–Littlewood conjectures · linear equations in primes · prime pairs · singular series
OP-00923 Open
The Hardy–Littlewood asymptotic formula for primes of the form m² + 1
NT · Hardy–Littlewood conjectures · Landau's problems · primes represented by polynomials
OP-00924 Open
Primes represented by a quadratic polynomial am² + bm + c
NT · Bunyakovsky conjecture · Hardy–Littlewood conjectures · primes represented by polynomials
OP-00925 Open
Representations n = am² + bm + p by a quadratic and a prime
NT · additive prime number theory · Hardy–Littlewood conjectures · quadratic polynomials
OP-00926 Open
Every large non-square is a prime plus a square
NT · additive prime number theory · Hardy–Littlewood conjectures · sums of a prime and a square
OP-00927 Open
Every large odd number is a prime plus twice a square
NT · additive prime number theory · Goldbach's other conjecture · Hardy–Littlewood conjectures
OP-00928 Open
Primes of the form m³ + k
NT · cubic residues · Hardy–Littlewood conjectures · primes represented by polynomials
OP-00929 Open
Every large non-cube is a prime plus a cube
NT · additive prime number theory · cubic residues · Hardy–Littlewood conjectures
OP-00930 Open
Primes of the form l³ + m³ + k
NT · cubic residues · Hardy–Littlewood conjectures · primes represented by polynomials · sums of cubes
OP-00931 Open
Asymptotic count of primes that are sums of three positive cubes
NT · cubic residues · Hardy–Littlewood conjectures · primes represented by polynomials · sums of cubes
OP-00932 Open
Prime pairs m² + 1, m² + 3
NT · Hardy–Littlewood conjectures · prime pairs · primes represented by polynomials
OP-00933 Open
Positive density of Ulam's sequence
NT · additive number theory · Ulam sequence · unique representations
OP-00934 Open
A Lipschitz function on the natural numbers whose graph has no three-term progression
CO · additive squares · arithmetic progressions · combinatorics on words
OP-00935 Open
Naïve corners in products of finite groups
CO · corners · density theorems · finite groups · quasirandom groups
OP-00936 Open
Rado's boundedness conjecture
CO · colourings · linear equations · partition regularity · Rado's theorem
OP-00937 Open
A long gap in a dilate of a square-root-sized set modulo a prime
NT · cyclic groups of prime order · dilates · gaps · polynomial method
OP-00938 Open
Additive bases of cyclic groups of nearly optimal size
NT · additive bases · cyclic groups · Sidon sets · sumsets
OP-00939 Open
Covering a cyclic group by few translates of a random set
CO · covering · cyclic groups of prime order · random sets · translates
OP-00940 Open
Density of linear covering codes of large radius
CO · coding theory · covering codes · Hamming balls · linear codes
OP-00941 Open
Residue classes modulo primes slightly above the square root
NT · Kakeya problem · large sieve · residue classes · sieve theory
OP-00942 Open
Covering every integer up to N ten times by one residue class per prime
NT · covering systems · Erdős problems · residue classes · sieve theory
OP-00943 Open
Cosets in A + A for sets with a small additive complement
CO · additive combinatorics · additive complements · Bogolyubov's lemma · finite field model · sumsets
OP-00944 Open
A composite number in a sumset below the square-root threshold
NT · inverse Goldbach problem · large sieve · primes · sumsets
OP-00945 Open
Every integer as a sum of two very smooth numbers
NT · binary additive problems · Erdős problems · friable integers · smooth numbers
OP-00946 Open
Sumsets of sets of squares grow by a power
NT · Rudin's conjecture · squares · sumsets · Λ(p) sets
OP-00947 Open
Small sets whose sumset contains the first n squares
NT · additive bases · Erdős problems · squares · sumsets
OP-00948 Open
Primes p for which p − 2 has an odd number of prime factors
NT · Liouville function · parity problem · shifted primes · twin primes
OP-00949 Open
A sum of two squares just below every large number
NT · gaps · Littlewood's problems · short intervals · sums of two squares
OP-00950 Open
Arcs in the plane over a prime field lie mostly on a cubic curve
CO · algebraic curves · arcs · finite geometry · no-three-in-line