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-2501 Higher Finiteness Embeddings and TDLC Analogues
- Math-2502 Chromatic Number of Overlapping Unit-Circle Constellations
- Math-2503 Borsuk Partition Problem in Dimensions Four Through Sixty-Three
- Math-2504 The Graphic Kahn–Kalai Conjecture
- Math-2505 Finite-field polynomial multiplication and integer-multiplication lower bounds
- Math-2506 Rigidity of Stable One-Phase Solutions
- Math-2507 The Generalized Étale-Homotopy Section Conjecture
- Math-2508 Existence of the Smith–Toda Complex $V(4)$
- Math-2509 Arthur-Langlands Reciprocity
- Math-2510 Low-Temperature Order in Quantum Heisenberg Ferromagnets
- Math-2511 AQFT Locality of Unitary Vertex Operator Algebras
- Math-2512 Structural Problems for $C^*$- and von Neumann Algebras
- Math-2513 Maximum Normalized Mahler Measure of Littlewood Polynomials
- Math-2514 Pointwise Convergence of Polynomial Ergodic Averages
- Math-2515 Rank Distribution in Quadratic-Twist Families
- Math-2516 Torsion-Anomalous Conjecture for Semiabelian Varieties
- Math-2517 Optimal Covering Density of Euclidean Balls
- Math-2518 Bounded-Diameter Monochromatic Covers
- Math-2519 Higher-dimensional Kakeya conjecture
- Math-2520 Median Actions and Residual Finiteness for Hyperbolic Groups with Sphere Boundary
- Math-2521 Pure-power Hilbert functions for complex Artinian complete intersections
- Math-2522 Lex-plus-powers Betti bounds for Artinian quotients over C
- Math-2523 Projectivity from simultaneous self-Ext and algebra-Ext vanishing
- Math-2524 A dimension-free quadratic bound for the canonical Foulkes–Howe map
- Math-2525 Complex group-ring traces vanish on infinite-order classes
- Math-2526 Deciding finite-algebra congruence-lattice representability
- Math-2527 Higher Verlinde fiber functors in positive characteristic
- Math-2528 Foulkes inclusion for the sixth symmetric power
- Math-2529 Integral block finiteness over a fixed complete valuation ring
- Math-2530 Integral K3 injectivity for regular local domains
- Math-2531 Integral K5 injectivity for regular local domains
- Math-2532 Finite central dimension of algebraic finitely generated division rings
- Math-2533 Finite torsion-class support for traces over l1 group algebras
- Math-2534 Finiteness of the little finitistic dimension
- Math-2535 Every irreducible occurs in the staircase tensor square
- Math-2536 Saturation factor one for even Spin groups
- Math-2537 An irreducible tensor square containing every symmetric-group representation
- Math-2538 Self-Ext vanishing over symmetric algebras
- Math-2539 Algebraicity of the prescribed Kuga–Satake map
- Math-2540 Algebraicity of split Weil-type eightfold classes
- Math-2541 All ordinary Kähler klt fourfold programs terminate
- Math-2542 All rational-boundary projective lc fourfold programs terminate
- Math-2543 Rank-preserving contraction for anticanonical fibrations
- Math-2544 Integral Bloch statement for surfaces of geometric genus zero
- Math-2545 Arithmetic Stein-degree bounds for log Calabi–Yau boundaries
- Math-2546 Bounded local klt complements for Fano contractions
- Math-2547 Bounded-metric anticanonical nonvanishing for klt pairs
- Math-2548 Bounded denominators in low-dimensional log Calabi–Yau fibrations
- Math-2549 Campana–Peternell for Fano sixfolds
- Math-2550 Abelianity of special compact Kähler fundamental groups