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-5401 A polarization--Fourier criterion for regular GNS cocycle representations
- Math-5402 Noncommutative Gamma_2 and sharp depolarizing curvature frontiers
- Math-5403 A dihedral symmetry barrier for noncrystallographic nonnesting
- Math-5404 A split source fragment and the dihedral noncrystallographic H-triangle
- Math-5405 Fuss-nonnesting orders, a rank-one obstruction, and a Boolean q-model
- Math-5406 A complement correction and a pointed type-B f/h identity
- Math-5407 Absolute-order topology, endpoint conventions, and an exact rank-two family
- Math-5408 A conjugacy-class coalgebra and Hopf completion for Cayley intervals
- Math-5409 Units, central splitting, and filtration for multivariable boxed convolution
- Math-5410 Signed-charge formulas for finite-order unitary cumulants
- Math-5411 Polytopality and an exact dihedral model for noncrystallographic associahedra
- Math-5412 Exceptional polygon models, a counting obstruction, and a folding certificate
- Math-5413 Generalized cluster complexes: solved topology and a simplicial thickening obstruction
- Math-5414 Higher Cohen-Macaulay connectivity of generalized cluster complexes
- Math-5415 Exact matrix recurrence and the irrational-exponent obstruction in noncrystallographic type
- Math-5416 Canonical supercharacter products: an exact divisibility criterion
- Math-5417 A prefix-cut obstruction for an NCQSym supercharacter realization
- Math-5418 Elementary characters generate Andre's supercharacter theory
- Math-5419 An elementary-generator characterization of the André–Yan theory
- Math-5420 Automorphism coarsenings and the reversal-quotient theory of U_n(q)
- Math-5421 Projected superinduction and the transitivity defect
- Math-5422 An abelianization supercharacter tower for Sylow subgroups of symmetric groups
- Math-5423 Borel supercharacters and a split torus-degree Hopf structure
- Math-5424 The dual NCSym realization and its internal coproduct
- Math-5425 A q-power-sum bridge to supercharacters and a block-interval-order model
- Math-5426 Induction from supercharacters to unipotent class functions of GL_n(q)
- Math-5427 Algebra-group supercharacter refinements and a class-two formula
- Math-5428 Affine hyperplane rank bounds and an explicit Veronese benchmark
- Math-5429 Fixed harmonic parts: exact low-degree breakpoints and a deformation criterion
- Math-5430 A reducible obstruction and the quadratic irreducible case
- Math-5431 Neighboring Newton edges and the corner-allocation obstruction
- Math-5432 A moment counterexample and a Levi wall for sphere links
- Math-5433 Formal and biholomorphic CR equivalence diverge
- Math-5434 Equivariant hyperquadric embeddings and a standard-parabolic obstruction
- Math-5435 A cohomological screen for Fefferman Pontryagin forms
- Math-5436 Literal and boundary counterexamples for Hermitian sums of squares
- Math-5437 Sharp 2-jet determination and an accumulation obstruction
- Math-5438 Boundary and Milnor obstructions to deformation into a ball
- Math-5439 LLT expansions in graded k-Schur functions: status, explicit families, and a normalization obstruction
- Math-5440 A generic clique-block basis of individual LLT polynomials
- Math-5441 The quotient and forced-lift dictionary for k-Schur and level-restricted structure constants
- Math-5442 A rigging-refined stable-level fusion polynomial
- Math-5443 A Garsia--Haiman filtration theorem and a small-k obstruction for diagonal harmonics
- Math-5444 Charge on LS galleries and paths
- Math-5445 Charge, the Brylinski--Kostant filtration, and canonical bases
- Math-5446 Symplectic duality and a complex-linearity obstruction for the Thurston metric
- Math-5447 Hausdorff noncomputability and a certified punctured-torus classifier
- Math-5448 Continuity of Thurston geodesic envelopes and diagonal collapse
- Math-5449 Endpoint and intrinsic symmetrizations of the Thurston metric
- Math-5450 Opposition-symmetric lifts and boundary scalarizations of the Thurston metric