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-5651 Scalar Curvature Question [?73]: [c] LetS be a Riemannian manifold homeomorphic to the connected sum of twenty copies ofS2× S2
- Math-5652 Reducibility of the holonomy of flat manifolds
- Math-5653 Manifolds modelled on flag manifolds — Question 2
- Math-5654 Area minimizing projective spaces in the projective space with the Berger metric
- Math-5655 Morse index of embedded minimal surfaces
- Math-5656 On the Hodge spectra of lens spaces
- Math-5657 Totally geodesic submanifolds and positive curvature
- Math-5658 Configuration Spaces of Tensegrities — Problem 2
- Math-5659 Configuration Spaces of Tensegrities — Problem 5
- Math-5660 Configuration Spaces of Tensegrities — Problem 6
- Math-5661 Configuration Spaces of Tensegrities — Problem 7
- Math-5662 Geometry of Curves and Surfaces — Problem 1.6
- Math-5663 Geometry of Curves and Surfaces — Problem 1.7
- Math-5664 Geometry of Curves and Surfaces — Problem 2.4
- Math-5665 Geometry of Curves and Surfaces — Problem 3.2
- Math-5666 Geometry of Curves and Surfaces — Problem 4.3
- Math-5667 Geometry of Curves and Surfaces — Problem 8.3
- Math-5668 For each arrangement of points in which the rectilinear crossing number is minimized, is the number of halving lines maximized
- Math-5669 What is the lowest number of faces possible for a holyhedron
- Math-5670 Wikipedia geometry item 78: Can every spherical non-convex polyhedron that tiles space by translation have its faces groupe…
- Math-5671 What constant $1.1 < a \leq 10.76$ governs the lower bound of a closed knot $K$'s minimum ropelength $L(K) \geq a\operatorname{Cr}(K)^{3/4}$
- Math-5672 Does every convex polyhedron have Rupert's property
- Math-5673 Is there a non-convex polyhedron without self-intersections with more than seven faces, all of which share an edge with each other
- Math-5674 One-Point Compactification for MF Spaces
- Math-5675 O33a — NP-hardness of binary quadratic Diophantine solvability
- Math-5676 Conjecture 1.8 — Langevin
- Math-5677 Conjecture 3.11 — $p$-adic analog of Lindemann-Weierstrass's Theorem
- Math-5678 Conjecture 3.12 — $p$-adic analog of an algebraic independence result of Gel’fond
- Math-5679 Conjecture 4.15
- Math-5680 Conjecture 4.18
- Math-5681 Fast evaluation of high-degree elliptic-curve isogenies
- Math-5682 Fast Tate–Lichtenbaum pairing computation
- Math-5683 Cup-product pairings in zeta computation
- Math-5684 Improved Frobenius lifts for nondegenerate curves
- Math-5685 Useful deformations for nondegenerate curves
- Math-5686 Nondegenerate surfaces in toric threefolds
- Math-5687 Factoring structured semiprimes from fewer known bits
- Math-5688 Factoring from nonconsecutive known bits
- Math-5689 Reducing guesses in factoring with known bits
- Math-5690 Faster Coppersmith root methods
- Math-5691 Polynomial-shape dependence in small-root algorithms
- Math-5692 Algebraic independence in multivariate elimination
- Math-5693 Distribution of elliptic-curve group structures
- Math-5694 Frequency of cyclic elliptic-curve groups
- Math-5695 Constructing an elliptic curve of prescribed order over a fixed field
- Math-5696 Effective representation of principally polarized abelian threefolds
- Math-5697 Faster pairing computation
- Math-5698 More MNT and pairing-friendly elliptic curves
- Math-5699 Pairing-friendly hyperelliptic curves
- Math-5700 Taxonomy of pairing-related assumptions