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-4451 Log K-Stability versus Geometric Invariant Theory
- Math-4452 Uniqueness of Scalar-Flat Kähler ALE Metrics
- Math-4453 Short-Time PIC1 Ricci Flow
- Math-4454 Singular Cardinal Arithmetic Without Weak Square
- Math-4455 Embedding Classification of Piecewise-Linear Interval Groups
- Math-4456 Stationary Reflection and Large Power at Aleph Omega
- Math-4457 Exotic Group $C^*$-Algebras for Nonamenable Locally Compact Groups
- Math-4458 Euler Characteristic and Coherence of Random Few-Relator Groups
- Math-4459 Coxeter Quotients of Automorphism Groups of Coxeter Groups
- Math-4460 Virtual Simplicity of Exotic Affine-Building Lattices
- Math-4461 Quasi-Isometric Rigidity of Acylindrical Hyperbolicity
- Math-4462 Comparison of Analytic and Periodic Cyclic Homology
- Math-4463 Extension of Group Cyclic Cocycles to Smooth Subalgebras
- Math-4464 Equivariant Derived Categories of Symplectic Surfaces
- Math-4465 Hard Lefschetz for Arbitrary $\ell$-Adic Sheaves
- Math-4466 Frobenius-Stable Loci and Dense Arithmetic Points
- Math-4467 Canonical Triple-Product $p$-Adic $L$-Values and Rational Points
- Math-4468 Boundary Branch Singularities of Area-Minimizing Currents
- Math-4469 Topology and Morse Theory of Allen-Cahn Moduli Spaces
- Math-4470 Infinite Transverse Actions on Codimension-One Foliations
- Math-4471 Natural Completions of Period Maps
- Math-4472 Projectivity of the Stein-Factorized Period-Map Completion
- Math-4473 Boundary-Corrected Ampleness of Extended Hodge Bundles
- Math-4474 Positivity of Log Canonical Bundles under Local Torelli
- Math-4475 Lower Bounds for Function-Field Quaternionic Periods
- Math-4476 Pointwise Function-Field Equidistribution from Period Integrals
- Math-4477 Sharp Moments of Zeta and Character Averages
- Math-4478 Sphere-Packing Bounds and Fourier Eigenfunction Constructions
- Math-4479 Subconvexity for Symmetric-Square L-Functions
- Math-4480 Maximum Complexity of Hyperplane Arrangement Levels
- Math-4481 Extremal Questions in Discrete Geometry and Topological Combinatorics
- Math-4482 Ranks of Reeb Action Spectra
- Math-4483 Transversal Foliations and Global Sections for Reeb Flows
- Math-4484 Nonlocal Water Waves with Generalized Vorticity
- Math-4485 Mean-Curvature Blowup Limits of Wings and Pitchfork Translators
- Math-4486 Explicit Cheeger Sets and Constants of Bounded Domains
- Math-4487 $C^1$ Regularity of Planar Convex Variational Minimizers
- Math-4488 Ancient Ovals as Post-Singularity Limit Flows
- Math-4489 Instantaneously Complete Yamabe Flow in Higher Dimensions
- Math-4490 Generalized Smith Questions for Compact Lie Groups
- Math-4491 Realizable Type Functions of Equivariant Spectra
- Math-4492 Small-Genus Cohomology of High-Dimensional Diffeomorphism Groups
- Math-4493 Equivariant Topological Modular Forms Duality for Compact Lie Groups
- Math-4494 Freely Complemented and Maximal Amenable MASAs
- Math-4495 Stable Rank One for Simple Reduced Group $C^*$-Algebras
- Math-4496 Realizing Lower Semicontinuous Trace Functions by Positive Elements
- Math-4497 Nonlinear Stability of Columnar Euler Vortices
- Math-4498 Realizability of Balanced Complexes as Tropical Varieties
- Math-4499 Grassmann Polytopes as Positive Geometries
- Math-4500 Cocircuit Graph Diameter Conjecture for Oriented Matroids