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-3701 Rigid Fano Targets of Holomorphic Maps
- Math-3702 Universal Fluctuation Limits for Exclusion Processes
- Math-3703 Circuits and Thresholds in Rank-Two Matrix Completion
- Math-3704 Non-Kähler Ricci Solitons and Broader Existence Methods
- Math-3705 Einstein Solvable Factors and Orthogonal Levi Orbits
- Math-3706 Convergence and Curvature of Homogeneous Ricci Flows
- Math-3707 Negative Ricci Curvature on Solvable Lie Algebras
- Math-3708 Compactness of Positively Curved Shrinking Ricci Solitons
- Math-3709 Periodic Topologically Simple Locally Compact Groups
- Math-3710 Essential Finite Generation of Valuation Rings
- Math-3711 Characteristic-Zero Lifts of Local Galois Extensions
- Math-3712 Minimal Coefficient Rings for Cyclic Local Lifts
- Math-3713 Classification of Local Oort Groups
- Math-3714 Odd Dihedral Groups as Oort Groups
- Math-3715 Triangle-Cone Characterization of Graphs
- Math-3716 Laplacian Spectra of Penrose Tiling Graphs
- Math-3717 Congruence from Complete Robin and Dirichlet Spectra
- Math-3718 Coarse Baum–Connes Failure without Embedded Expanders
- Math-3719 Finitely Presented Counterexamples for Conjugation-Invariant Norms
- Math-3720 Countable Groups of Prescribed Transitivity Degree
- Math-3721 Equality Cases in the Balanced Lower Bound Conjecture
- Math-3722 Bagchi’s Lower Bound for Triangulated Manifolds
- Math-3723 Uniqueness of the Bryant–Salamon $G_{2}$ Metric on the Spin Bundle
- Math-3724 ACM Line Configurations and Symbolic Initial Degrees
- Math-3725 Curves with Minimal Symbolic Initial-Degree Gap
- Math-3726 Extremal Fat-Point Initial Degrees and Star Configurations
- Math-3727 Hopf Algebra Extensions and Their Conformal Field Theories
- Math-3728 Finite Fourier Feedback for Driftless-System Stabilization
- Math-3729 Trigonometric-Polynomial Feedback for Nonlinear Stabilization
- Math-3730 Commuting Billiard Maps and Confocal Ellipses
- Math-3731 Reconstruction and Response Sets of AC Networks
- Math-3732 Dihedral Rigidity and Offsets of Nonconvex Polytopes
- Math-3733 Mirror Conifold Transitions and Analytic Smoothings
- Math-3734 Mirror Classification of Orbifold Del Pezzo Surfaces
- Math-3735 Period Conjectures for Fano Polygons and Del Pezzo Surfaces
- Math-3736 Conformal Field Theories Representing TMF Classes
- Math-3737 Finiteness of Automorphism Groups of Rational Vertex Operator Algebras
- Math-3738 Diagrammatic Actions on Principal Tilting Categories
- Math-3739 Maximal Real Betti Numbers of Tridegree Surfaces
- Math-3740 Steinberg Tensor Products with Good Filtrations
- Math-3741 Topological Period–Index Conjecture
- Math-3742 Restriction Criteria for Endotrivial Modules
- Math-3743 Categorical Diagonalization of Coxeter Full Twists
- Math-3744 Common Triangular Bases for Quantum Cluster Algebras
- Math-3745 K-Theoretic Geometric Satake Equivalence
- Math-3746 Characteristic Varieties of Rigid-Analytic D-Modules
- Math-3747 Minimal Rational Curves on Complete Symmetric Varieties
- Math-3748 Spectral Norms of Gaussian Matrices with Variance Profiles
- Math-3749 Rigidity of Continuous Orbit Equivalence
- Math-3750 Helton's Sum-of-Squares Theorem for Low-Dimensional Group Rings