Top Open Problems
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-2301 Word problem for arbitrary Artin groups
- Math-2302 Algorithms for the word problem in Artin groups
- Math-2303 Second homotopy of Artin classifying complexes
- Math-2304 Parabolic subgroup intersections in Artin groups, including Euclidean type
- Math-2305 Parabolic intersections under nonpositive curvature assumptions
- Math-2306 Finitely presented infinite simple amenable groups
- Math-2307 The virtually-nilpotent/free-semigroup alternative
- Math-2308 Existence of infinite finitely presented torsion groups
- Math-2309 Universal optimality beyond rapidly decaying completely monotone potentials
- Math-2310 ALE singularities: Type-II existence and a bounded-scalar scale-energy certificate
- Math-2311 Finite traceless-Ricci budget and Ricci-flat bubbles under bounded scalar curvature
- Math-2312 Endpoint Ricci-energy balance and Weyl-dominated blow-ups under bounded scalar curvature
- Math-2313 A hyperbolic geodesic and the robust infinite branch
- Math-2314 Closed geodesics in a finite-volume torus ansatz
- Math-2315 No conjugate points: flat-growth rigidity and the three-dimensional residue
- Math-2316 One-equation reductions for the rational Hamilton quaternions and Lipschitz order
- Math-2317 Finite-fiber normalization for elliptic Diophantine encodings
- Math-2318 Characterization of cones admitting lifted LMI representations
- Math-2319 Polynomial-time lifted LMI representations of convex cones
- Math-2320 Long-time existence and behavior of the Calabi flow
- Math-2321 Boundary integrability and the explicit confocal-caustic dictionary
- Math-2322 Non-self-adjoint spectral theory: completeness, reconstruction, and matrix-function bounds
- Math-2323 The Dirac-Brown invariant-subspace problem: a defect-attainment reduction
- Math-2324 An arithmetic and angular reduction for the 3-4-5 triangular billiard
- Math-2325 Directional and interval-exchange reductions for polygonal billiards
- Math-2326 Strongly Balanced Almost-Uniform Vector Permutations
- Math-2327 Bounded Complements for $\varepsilon-Log-Canonical$ Varieties
- Math-2328 Strong Nakayama Conjecture
- Math-2329 Linear-Programming Sharpness and Universal Lattice Optimality
- Math-2330 Arithmetic-Formula Lower Bounds for Permanent and Determinant
- Math-2331 Baum–Connes Conjecture for Locally Compact Groups
- Math-2332 Birch–Swinnerton-Dyer Conjecture
- Math-2333 Baum–Connes Conjecture for Torsion-Free Groups
- Math-2334 Z-Stability of Infinite Tensor Powers
- Math-2335 Singularity Probability of Random Symmetric Sign Matrices
- Math-2336 Limit Theorems for Random Walks in Random Environments
- Math-2337 Bloch–Beilinson Torsion Conjecture for Albanese Kernels
- Math-2338 Nonvanishing or Uniruledness for Smooth Projective Varieties
- Math-2339 Birkhoff Integrable-Billiards Conjecture
- Math-2340 Affine Fibrations as Affine-Space Bundles
- Math-2341 Higher-Dimensional Cancellation for Affine Domains
- Math-2342 Stable Coordinate Conjecture for Complex Polynomials
- Math-2343 Caccetta–Häggkvist Conjecture for Directed Triangles
- Math-2344 Single-Solution Bounds for Diophantine Equations
- Math-2345 Artin’s Primitive-Root Density for Two
- Math-2346 Primitive-Root Density Formulas for Rank-One Tori
- Math-2347 Parity Conjectures for Elliptic Curves over Number Fields
- Math-2348 Pálfy–Pudlák Finite-Lattice Representation Problem
- Math-2349 RSW Theory for Anisotropic Square-Lattice Percolation
- Math-2350 Ramsey Sets and Finite Transitive Embeddings