Mathematics
Open problems, research attempts and community review.
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-4551 Extrapolating Clusterings from Semidefinite Subsamples
- Math-4552 Local Approximation of Random-Graph Semidefinite Programs
- Math-4553 Uniqueness of Equilibria in Rank-One Bimatrix Games
- Math-4554 Proximity and Sparsity of Optimal Integer Solutions
- Math-4555 Convergence Rates for Convex-Body Bounds
- Math-4556 Fast Low-Rank Maximum-Weight Assignment
- Math-4557 Integrality Gaps for Directed Linear k-Cut
- Math-4558 Hardness of Root-Dependent Spanning-Tree Optimization
- Math-4559 Hardness of Path-Cost Arborescence Optimization
- Math-4560 Polynomial-Time Comparison of Sparse Algebraic Power Sums
- Math-4561 Degree-Utility Optimization in Graphs
- Math-4562 Real Tau Conjecture for Depth-Four Circuits
- Math-4563 Karchmer–Raz–Wigderson Composition Conjecture
- Math-4564 Subquadratic Approximation for Longest Common Subsequences
- Math-4565 Geometric Explanations and Polynomial Pivot Rules for Simplex
- Math-4566 Sharp Smoothed Complexity of Simplex Pivot Rules
- Math-4567 Theta Invariants and New Families of MRD Codes
- Math-4568 Explicit RIP Matrices Beyond Square-Root Sparsity
- Math-4569 Square-Root Sparsity for Explicit RIP Matrices
- Math-4570 Sample Complexity of Vertex-Distribution-Free Graph Testing
- Math-4571 Complexity of Approximate Counting in Spin Systems
- Math-4572 Exact Higher-Order Matrix Decomposability
- Math-4573 Semidefinite Hierarchies for Equiangular Line Bounds
- Math-4574 Computational Recognition of Polytope Face Vectors and Cones
- Math-4575 Recognition of Virtually Special Hyperbolic Three-Manifolds
- Math-4576 Minimum Crossing Realizations of Spatial Polygon Angle Sequences
- Math-4577 Submultiplicativity Gaps for Stabilizer Extent
- Math-4578 Complexity of Submodular $k$-Partition
- Math-4579 Integer Programming with Bounded Subdeterminants
- Math-4580 Extension Complexity of Inscribed Fixed-Dimensional Polytopes
- Math-4581 Arborescences Induced by Linear-Programming Pivot Rules
- Math-4582 Near-Optimal Algorithms for Mixed-Integer Convex Optimization
- Math-4583 Linear Bounds for Minimally Integer-Infeasible Systems
- Math-4584 Approximating Maximum Nonsymmetric Principal Subdeterminants
- Math-4585 Better-Than-Two Approximation for Multiplicative Connectivity Augmentation
- Math-4586 Balanced Signings in the Subtour Polytope
- Math-4587 Compact Representations of Four-Thirds Near-Mincuts
- Math-4588 Better Approximations for Unrelated Graph Balancing
- Math-4589 Deterministic Optimization of Top-$k$ Perfect-Matching Edges
- Math-4590 Property Testing for Noncommutative Quantum Functions
- Math-4591 Algebraic and Graph-Property Tests for Quantum Functions
- Math-4592 Canonical Paths Versus Spectral Independence
- Math-4593 Good Locally Testable Quantum Codes and Linear-Rate PCPs
- Math-4594 Convergence and Effective Rates of Unwinding Series
- Math-4595 Phase Retrieval from Gabor and Wavelet Magnitudes
- Math-4596 Optimal Neural-Network Depth for Sparse Recovery
- Math-4597 LOCAL Coloring Complexity and Constant-Round Decidability on Trees
- Math-4598 Algebraic Complexity of Borel Constraint Problems
- Math-4599 Determinacy Methods in LOCAL and Borel Coloring
- Math-4600 Local-to-Global Tensorization of Information Functionals