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-2401 Minimum Graph Homomorphism Counts at Fixed Density
- Math-2402 Displacement Exponents for Low-Dimensional Self-Avoiding Walks
- Math-2403 Lefschetz Classes and the Tate and Hodge Conjectures
- Math-2404 Rigidity of Completely Close $C^*$-Algebras
- Math-2405 Regularity Properties of Nuclear $C^*$-Algebras
- Math-2406 Homogeneity of Fano Contact Manifolds
- Math-2407 Sidorenko's Inequality for Bipartite Graphs
- Math-2408 Linear Cycle-and-Edge Decompositions of Graphs
- Math-2409 Nonsingularity and Limit Laws for Random Matrices
- Math-2410 Almost-Everywhere Fourier Convergence in $L^{1}$
- Math-2411 Fujita's Global Generation and Very-Ampleness Conjecture
- Math-2412 Enumeration of Graphs with Prescribed Degree Sequences
- Math-2413 Spectrahedrality of Hyperbolicity Cones
- Math-2414 Vanishing of the $hat A$-Genus Under Nonnegative Curvature
- Math-2415 Gromov Macroscopic Dimension Conjecture
- Math-2416 Abundance Conjecture for Projective Minimal Models
- Math-2417 Rational Curves on Compact Kähler Manifolds
- Math-2418 Solvability of Group Equations and Surjectivity of Word Maps
- Math-2419 The mod-$\ell$ Bogomolov–Pop conjecture
- Math-2420 The chromatic splitting conjecture
- Math-2421 Chromatic Splitting of the Local Sphere
- Math-2422 Chromatic Fiber Structure at Bad Primes
- Math-2423 Bogomolov–Gieseker Inequality for Tilt-Semistable Threefold Complexes
- Math-2424 Strong Locality and Reconstruction of Vertex Operator Algebras
- Math-2425 Eigenvalue Counts for Low-Degree Random Regular Graphs
- Math-2426 Injectivity of the Baum–Connes Assembly Map
- Math-2427 Strong Cosmic Censorship at Weak Regularity
- Math-2428 Full-Measure Families of Ergodic Irrational Polygons
- Math-2429 Petty's projection-body conjecture
- Math-2430 Color Savings and Strong Chromatic Index Bounds
- Math-2431 Packing and Covering for Infinite Matroids
- Math-2432 Stanley–Stembridge Chromatic Symmetric Function Conjecture
- Math-2433 Polynomial Algorithms for Mean-Payoff Games and Linear Programming
- Math-2434 Hemisphere Partition Functions and Stability Across GLSM Phases
- Math-2435 Donovan’s Finiteness Conjecture for Fixed Defect Groups
- Math-2436 Multistationarity and Permanence in MESSI Reaction Networks
- Math-2437 Absolute Continuity Parameters for Bernoulli Convolutions
- Math-2438 Real Baum–Connes Isomorphism Conjecture
- Math-2439 Finiteness of Atypical Hodge Subvarieties
- Math-2440 Universal Bounds on Atomic Excess Charge
- Math-2441 Lech Multiplicity Conjecture for Flat Local Extensions
- Math-2442 Amenability of Thompson Group and Interval Homeomorphism Groups
- Math-2443 Finiteness of Optimal Points in Shimura Subvarieties
- Math-2444 Persistence and Permanence of Weakly Reversible Reaction Networks
- Math-2445 $L^p$ Bounds for the Triangular Hilbert Transform
- Math-2446 Cartan–Hadamard Isoperimetric Conjecture
- Math-2447 Universal-Cover Decomposition for Nef Anticanonical Manifolds
- Math-2448 Kobayashi Pseudometric Vanishing on Calabi–Yau Manifolds
- Math-2449 Generalized Riemann Hypothesis for Automorphic L-Functions
- Math-2450 Nuclear Dimension of Transformation-Group Crossed Products