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-4701 Equivalence of Dual Pisot Substitution Constructions
- Math-4702 Absence of Eigenvalues for Pisot Substitution Operators
- Math-4703 Semiclassical Correspondence of Primitive and Poisson Spectra
- Math-4704 Local Closedness of Symplectic Cores
- Math-4705 Poisson Dixmier–Moeglin Equivalence
- Math-4706 Yangian Realization of Universal Affine Verma Modules
- Math-4707 Cluster Monomials and Simple Quantum Affine Modules
- Math-4708 Stable Low-Rank Matrix Completion from Random Samples
- Math-4709 Cellular Models for Unequal Parameter Hecke Algebras
- Math-4710 Rigidity Under Stable Equivalence of Quantum Complete Intersections
- Math-4711 Classification of Analytic Hilbert Modules on Strictly Convex Domains
- Math-4712 Extremal Tuples of Commuting Contractions
- Math-4713 Fujiki-Class Limits of Kähler Manifolds
- Math-4714 Kähler Limits and Transcendental Morse Inequalities
- Math-4715 Relative Betti Inequalities for Lex-Plus-Powers Ideals
- Math-4716 Regularity Bounds for Ext Modules Under Serre Conditions
- Math-4717 Symbolic Rees Rings and Nagata’s Conjecture
- Math-4718 Uniform Generic Degree Bounds for Ideal Membership
- Math-4719 Coloring $F$-Free Uniform Hypergraphs
- Math-4720 Vickrey Costs in Random Combinatorial Optimization
- Math-4721 Matrix Factorization over Curve Patching Fields
- Math-4722 Local–Global Principles for Homogeneous Spaces
- Math-4723 Anisotropic Bilinear Forms in Characteristic Two
- Math-4724 Cohomology Classes of Undistorted Central Extensions
- Math-4725 Stable Cohomology of Higher-Dimensional Diffeomorphism Groups
- Math-4726 Compression, Amenability, and Uniform Embeddability of Groups
- Math-4727 Arithmetic Intersection Formula for Special Cycles
- Math-4728 Iwasawa Main Conjecture for Dihedral Ring Class Towers
- Math-4729 Kato–Suslin Homology of Smooth Connected Varieties
- Math-4730 Left Exactness of n-Motivic Sheaf Inclusions
- Math-4731 Generalized Fermat Equation $a^3+b^3=c^n$
- Math-4732 Frobenius Polynomials of Degeneration Pencils
- Math-4733 Algebraicity of Complex ATR Points
- Math-4734 Shimura Period Relations for Jacquet–Langlands Transfers
- Math-4735 Radius and Fixed Points of Convex Building Subsets
- Math-4736 Quantization of Concentration Mass for Higher-Order Equations
- Math-4737 Monochromatic Arm Exponents in Critical Percolation
- Math-4738 Largest Critical Percolation Clusters with Free Boundaries
- Math-4739 Equivalence of Sznitman Ballisticity Conditions
- Math-4740 Gaussian Central Limits for Stationary Sequences
- Math-4741 Power Variations of Volatility-Modulated Gaussian Processes
- Math-4742 Homotopy Invariance of Algebraic K-Theory for Group Rings
- Math-4743 Baum–Connes Theory for Non-Hausdorff Groupoids
- Math-4744 Symplectic Singularities from Symplectic Reduction
- Math-4745 Infinitesimal-Fiber Criteria for Isomorphisms of Scheme Germs
- Math-4746 Allowed Differential Forms and Monodromy Eigenvalues
- Math-4747 Infinite-Topology Types of Embedded Minimal Surfaces
- Math-4748 Rigidity of Complete Embedded Minimal Surfaces
- Math-4749 SRB Measures for Piecewise-Affine Hyperbolic Systems
- Math-4750 Meromorphic Ruelle Zeta Functions for Piecewise Hyperbolic Systems