Computational algebra and number theory
The Top Open Problems editorial order restricted to Computer Science, followed by cross-listed economics entries. Existing relative order is retained, with provisional placements for new game-learning questions; most entries have no individual difficulty assessment. About rankings
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- CS-307 Orbit-Closure Obstructions for Permanent–Determinant Separation
- CS-309 Symmetry-Preserving Evaluation of Orbitwise Generating Functions
- CS-337 Complexity of Bray’s Involution-Centralizer Algorithm
- CS-338 Sublinear Membership Testing in Two-Generator Matrix Groups
- CS-339 Computing Hecke Operators for Arithmetic-Group Cohomology
- CS-340 Security of Interactive Lattice-Based Group Key Exchange
- CS-358 Polynomial-Time Comparison of Sparse Algebraic Power Sums
- CS-370 Exact Higher-Order Matrix Decomposability
- CS-388 Property Testing for Noncommutative Quantum Functions
- CS-389 Algebraic and Graph-Property Tests for Quantum Functions
- CS-396 Algebraic Complexity of Borel Constraint Problems
- CS-413 Algorithms for Amoeba Dimensions from Tropical Fans
- CS-418 Fractional Coefficient Savings in Algebraic Proof Systems
- CS-419 Circuit-Size Hierarchy in Bounded Arithmetic
- CS-428 Quasilinear Finite-Field Polynomial Multiplication
- CS-438 Complexity-Bounded Computation of Maximum Destabilizing Subgroups
- CS-440 Freeness of Two-Generator Integral Matrix Groups
- CS-442 Zero Submatrices in Sparse Low-Rank Matrices
- CS-443 Optimal Bounds for Pairs of Commuting Integer Matrices
- CS-449 Smale's 4th Problem: Integer Zeros of Polynomials
- CS-475 Degree-two-and-three Markov basis for the Birkhoff ranking model
- CS-483 Algebraic fibers and sharp sets for missing categorical data
- CS-484 Determinantal certificates for safe categorical collapse before multiple imputation
- CS-492 A precise probabilistic repair and algebraic criteria for interval cell spectra
- CS-496 Algebraic certificates for nonparametric mixture likelihood
- CS-500 Gaussian conditional independence as an algebraic minor
- CS-501 Two-sided novelty certificates for sparse binomial output
- CS-502 A scale-normalized robustness criterion for algebraic design fans
- CS-505 Rank-profile compression for finite-field time-series models
- CS-507 Specialized algebra kernels and certified interoperability
- CS-508 Faithful interchange between computational algebra systems
- CS-509 A certificate-first algebraic layer for R
- CS-512 Deformation transport, Fesenko transforms, and a Riemann--Roch size barrier
- CS-513 A format-sensitive genus barrier for Schoof-Pila
- CS-514 Fields, orbits, and explicit torsion points
- CS-515 Length-faithful algebraic and group-theoretic parameter screens for SL_n(F_p) hashing
- CS-524 Explicit near-minimal units from the golden-ratio radical
- CS-567 A semantics-bound certified bridge between Lean and computer algebra
- CS-607 A deterministic contract for parallel Macaulay2 core routines
- CS-608 Certified portfolios for a responsive Macaulay2 top level
- CS-609 A degree-slice fast path for basis
- CS-610 Certified degree windows for truncated algebra commands
- CS-611 A versioned contract for reproducible Macaulay2 family benchmarks
- CS-612 Simplicial resolutions in Macaulay2 and a join-complete verification contract
- CS-613 Truncation representatives, semantic equality certificates, and functorial cohomology maps
- CS-629 Semaev's Auxiliary Elliptic-Curve Index-Calculus Algorithm
- CS-642 Resolved Triple-Product Group Challenge
- CS-643 Space-Efficient Lattice-Basis Reduction
- CS-652 Boolean Evaluation and Arithmetic-Circuit Complexity
- CS-653 Antisymmetric Association Schemes and Polynomial Factoring