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-13 Permanent versus Determinant over C
- CS-14 Permanent–Determinant Separation Through Geometric Complexity Theory
- CS-15 Derandomization of Polynomial Identity Testing
- CS-46 Omega(n log n) Boolean Circuit Lower Bound for Integer Multiplication
- CS-72 Real $\tau$-Conjecture for Sparse Polynomial Sums and Products
- CS-92 Discrete Logarithm Problem
- CS-108 Finite-field factorization and sparse-polynomial root testing
- CS-109 Prime-factor advice in power-residue quotients
- CS-110 Three zeta-like products, degree-count inversion, and the factorization boundary
- CS-111 Arithmetic-Formula Lower Bounds for Permanent and Determinant
- CS-112 Decidability of Rational Points over Number Fields
- CS-117 Finite-field polynomial multiplication and integer-multiplication lower bounds
- CS-125 Complex square and rectangular multiplication bounds
- CS-138 Integer multiplication below n log n
- CS-145 Hitting lists for noncommutative rational formulas
- CS-152 Cubic border-determinantal lower bound for the permanent
- CS-155 Matrix hitting points in every positive characteristic
- CS-159 One rational matrix hitting point for noncommutative formulas
- CS-192 Linear collapse, binomial hypersurfaces, and the image of local-odds fibers
- CS-196 An algebraic one-mode certificate for MANOVA
- CS-200 Transcendence-aware algebraic localization of symmetric Gaussian-mixture modes
- CS-206 A cyclic-slice chart for balanced minimal border rank
- CS-209 Root obstruction and outgroup-oriented algebraic clade certificates
- CS-222 Nondefectivity and low-degree obstructions for the two-component S4 Birkhoff model
- CS-227 Finite-field least squares as statistical decoding
- CS-228 Cyclic-binomial structure in an early Agrawal conjecture
- CS-229 A norm obstruction for Agrawal's conjecture
- CS-230 Perfect-number recognition and simultaneous polynomial divisors
- CS-231 Adjacent nonisogenous fibers in the Legendre family
- CS-232 Irreducible line sections: exact convention-sensitive counts and monodromy status
- CS-233 Binomial windows for prescribed-degree factors
- CS-234 Information and conditioning audit for zeta-zero primality and factoring proposals
- CS-235 A local-to-global screen for number-field ECM torsion
- CS-236 Geometry, residues, and scale thresholds for prescribed-prefix prime products
- CS-237 A nonresidue-to-witness reduction and exact witness count
- CS-238 Finite certificate interfaces for finite-field zeta functions
- CS-239 Deformation, specialization, and plane-curve genus
- CS-240 Deterministic roots of X^3-2: a density-one-eighteenth residual envelope
- CS-258 HHL, Macaulay conditioning, and presentation instability
- CS-260 A localization-safe action of Weyl operators
- CS-261 Degree-windowed Cech computation and the role of one b-function
- CS-262 Fixed-ambient extraction of roots of finite Frobenius modules
- CS-263 Random-access slices of free resolutions
- CS-264 A fixed-basis semibasis certificate for DG-module interoperability
- CS-265 Degree-local Hom computation and certified corner reuse
- CS-272 Polynomial-Time Computation of Ehrhart Periods
- CS-275 Polynomial Complexity of Greedy Lattice Reduction
- CS-280 Quantum Hardness of Approximate Lattice Problems
- CS-289 Optimal Algebraic Immunity of Boolean Functions
- CS-290 Explicit Polynomial Maps Escaping Low-Degree Images