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-6801 Discrete First Cohomology of Totally Disconnected Groups
- Math-6802 TDLC Analogue of Finite-Subgroup Conjugacy
- Math-6803 Ultra-Log-Concavity from a Matrix Recursion
- Math-6804 Positive Weighted $h^*$-Polynomials beyond Product Weights
- Math-6805 Bounded-Variation Solutions for Continuum Traffic Models
- Math-6806 Post-Lie Structures with Semisimple Target
- Math-6807 Jordan Brackets and Simple Transposed Poisson Algebras
- Math-6808 BV Structures with Nonsemisimple Nakayama Automorphisms
- Math-6809 Poisson Nilpotency and Solvability in Small Characteristics
- Math-6810 Finite Axiomatizability of TEIP over Open Induction
- Math-6811 Positivity Criterion for Quantum Greedy Bases
- Math-6812 Rationality of Separable Permutation Subclasses
- Math-6813 Counting-Sequence Ratios for Length-Six Principal Classes
- Math-6814 Structural Decomposition of Separable Permutation Subclasses
- Math-6815 Generating-Function Field for Separable Permutation Subclasses
- Math-6816 Combinatorial Interpretations of Negative k-Arrangements
- Math-6817 Monotone k-Shuffles in Long Permutations
- Math-6818 Valuation Bounds When the Center Meets the Negative Part
- Math-6819 Dolnikov’s Colorful Transversal Conjecture
- Math-6820 Simultaneous Embeddings of Random Planar Graphs
- Math-6821 No-Three-in-Line Problem
- Math-6822 Face-Size Distribution in Random Pseudoline Arrangements
- Math-6823 Finiteness of Generalized Moore Graphs
- Math-6824 Extremal Bipartite Containment of B-t
- Math-6825 Dihedral-Angle Gaps and Box-Graph Independence
- Math-6826 Sharper Positive-Scalar-Curvature Face Gluing
- Math-6827 Probabilistic Growth Methods for Linear Algebraic Groups
- Math-6828 Diameter Bounds with Permutation-Rich Generating Sets
- Math-6829 Conjugacy-Class Intersections with Generating Sets
- Math-6830 Shadowing Without Bounded Distortion
- Math-6831 Weighted-Shift Supercyclicity Converse
- Math-6832 $\Gamma$-Supercyclicity of Composition Operators and Weighted Shifts
- Math-6833 Hochschild and Categorical Entropy in dg Dynamics
- Math-6834 Quantum-Channel Interpolation Characterization
- Math-6835 Unitary Integral Identity for Noncommutative Polynomials
- Math-6836 Uniform Determinant Integrals for Row Contractions
- Math-6837 Free Polar Decomposition Under a Nondegeneracy Condition
- Math-6838 Infinite-Resolution Random-Surface Question
- Math-6839 Wishart Processes with Noninjective Semigroups
- Math-6840 Positivity and Convergence of a Splitting Scheme
- Math-6841 Splitting Schemes for Rough Stochastic Heat Equations
- Math-6842 Welschinger Specialization of Generalized Block–Göttsche Polynomials
- Math-6843 Strong Geography for Rational Homology Spheres
- Math-6844 Triviality of the Parametrized-Surgery Class on $S^4$
- Math-6845 Kähler Shafarevich-Tate Twists
- Math-6846 Stability Conditions from Surface Degenerations
- Math-6847 Positive-Entropy Automorphisms of Strict Calabi-Yau Threefolds
- Math-6848 Tail-Dependence Estimators Under Long-Range Dependence
- Math-6849 Stable Reduction of Plane Quartics from Cayley Octads
- Math-6850 Brauer Groups of Tame Stacky Curves