Computational algebra and number theory
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-4496 Orbit-Closure Obstructions for Permanent–Determinant Separation
- Math-4498 Symmetry-Preserving Evaluation of Orbitwise Generating Functions
- Math-4526 Complexity of Bray’s Involution-Centralizer Algorithm
- Math-4527 Sublinear Membership Testing in Two-Generator Matrix Groups
- Math-4528 Computing Hecke Operators for Arithmetic-Group Cohomology
- Math-4529 Security of Interactive Lattice-Based Group Key Exchange
- Math-4547 Polynomial-Time Comparison of Sparse Algebraic Power Sums
- Math-4559 Exact Higher-Order Matrix Decomposability
- Math-4577 Property Testing for Noncommutative Quantum Functions
- Math-4578 Algebraic and Graph-Property Tests for Quantum Functions
- Math-4585 Algebraic Complexity of Borel Constraint Problems
- Math-4602 Algorithms for Amoeba Dimensions from Tropical Fans
- Math-4607 Fractional Coefficient Savings in Algebraic Proof Systems
- Math-4608 Circuit-Size Hierarchy in Bounded Arithmetic
- Math-4617 Quasilinear Finite-Field Polynomial Multiplication
- Math-4627 Complexity-Bounded Computation of Maximum Destabilizing Subgroups
- Math-4629 Freeness of Two-Generator Integral Matrix Groups
- Math-4631 Zero Submatrices in Sparse Low-Rank Matrices
- Math-4632 Optimal Bounds for Pairs of Commuting Integer Matrices
- Math-4984 Smale's 4th Problem: Integer Zeros of Polynomials
- Math-5010 Degree-two-and-three Markov basis for the Birkhoff ranking model
- Math-5018 Algebraic fibers and sharp sets for missing categorical data
- Math-5019 Determinantal certificates for safe categorical collapse before multiple imputation
- Math-5027 A precise probabilistic repair and algebraic criteria for interval cell spectra
- Math-5031 Algebraic certificates for nonparametric mixture likelihood
- Math-5035 Gaussian conditional independence as an algebraic minor
- Math-5036 Two-sided novelty certificates for sparse binomial output
- Math-5037 A scale-normalized robustness criterion for algebraic design fans
- Math-5040 Rank-profile compression for finite-field time-series models
- Math-5042 Specialized algebra kernels and certified interoperability
- Math-5043 Faithful interchange between computational algebra systems
- Math-5044 A certificate-first algebraic layer for R
- Math-5047 Deformation transport, Fesenko transforms, and a Riemann--Roch size barrier
- Math-5048 A format-sensitive genus barrier for Schoof-Pila
- Math-5049 Fields, orbits, and explicit torsion points
- Math-5050 Length-faithful algebraic and group-theoretic parameter screens for SL_n(F_p) hashing
- Math-5059 Explicit near-minimal units from the golden-ratio radical
- Math-5102 A semantics-bound certified bridge between Lean and computer algebra
- Math-5142 A deterministic contract for parallel Macaulay2 core routines
- Math-5143 Certified portfolios for a responsive Macaulay2 top level
- Math-5144 A degree-slice fast path for basis
- Math-5145 Certified degree windows for truncated algebra commands
- Math-5146 A versioned contract for reproducible Macaulay2 family benchmarks
- Math-5147 Simplicial resolutions in Macaulay2 and a join-complete verification contract
- Math-5148 Truncation representatives, semantic equality certificates, and functorial cohomology maps
- Math-5164 Semaev's Auxiliary Elliptic-Curve Index-Calculus Algorithm
- Math-5177 Resolved Triple-Product Group Challenge
- Math-5178 Space-Efficient Lattice-Basis Reduction
- Math-5187 Boolean Evaluation and Arithmetic-Circuit Complexity
- Math-5188 Antisymmetric Association Schemes and Polynomial Factoring