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-5601 Nilpotent groups
- Math-5602 Sharp Lichnerowicz theorem
- Math-5603 Local assumptions for concentration
- Math-5604 Discrete sectional curvature
- Math-5605 L2 Bonnet–Myers and dimension
- Math-5606 Kolmogorov mixing-torus problem
- Math-5607 Mather theory near integrable systems
- Math-5608 Entropy and Deligne periods
- Math-5609 Pingree open problems — Hochman problem 1
- Math-5610 Pingree open problems — Petersen tail-field problem 1
- Math-5611 Pingree open problems — Petersen tail-field problem 2
- Math-5612 Pingree open problems — Ledrappier problem 1
- Math-5613 Embedding under a preimage bound
- Math-5614 Salem beta-transformations
- Math-5615 Types of vertices of reachable polygons
- Math-5616 Reachable points lie on reachable polygons
- Math-5617 Reachable points on lines through a unitary pair
- Math-5618 Types of parallel short trajectories
- Math-5619 Length ratios of parallel short trajectories
- Math-5620 Short geodesics on the regular dodecahedron
- Math-5621 Elliptic-billiard invariant k_{109}
- Math-5622 Elliptic-billiard invariant k_{802}
- Math-5623 Elliptic-billiard invariant k_{907,a}
- Math-5624 Elliptic-billiard invariant k_{907,b}
- Math-5625 Angle and renormalization at the golden-mean Siegel critical point
- Math-5626 Degenerate-flow limits of bad Newton polynomials
- Math-5627 Uniform access to roots for relaxed Newton maps
- Math-5628 Vertex $\pi$-Floodlights
- Math-5629 Freeze-Tag: Optimal Strategies for Awakening a Swarm of Robots
- Math-5630 Rigidity of Smooth Isometric Families of Compact Surfaces
- Math-5631 Extension into a Complete Hermitian Ball
- Math-5632 Isothermal Coordinates for Affine Minimal Surfaces
- Math-5633 Curvature-Type Tensors of Statistical Manifolds
- Math-5634 Tangent-Bundle Symplectic and Almost Complex Structures
- Math-5635 Integrable Radial Distributions and One-Conformal Flatness
- Math-5636 Inflection Points of Projectively Flat Curves
- Math-5637 Affine Vertices and Inflection Points
- Math-5638 Boundaries of Groups and Kleinian Groups — Problem 49
- Math-5639 Boundaries of Groups and Kleinian Groups — Problem 63
- Math-5640 Boundaries of Groups and Kleinian Groups — Problem 80
- Math-5641 Boundaries of Groups and Kleinian Groups — Problem 82
- Math-5642 Boundaries of Groups and Kleinian Groups — Problem 89
- Math-5643 D. Damanik: Quantum Mechanics and Quasicrystals — Conjecture
- Math-5644 Scalar Curvature Question [?18]: Let $X_{\mathrm{fl}}=\mathbb{R}^n/\Gamma$ be a complete flat manifold whose group $\Gamma$ acts by parallel tr
- Math-5645 Scalar Curvature Question [?24]: (i) It is unclear if the last step in the above argument is truly needed: conceivably, maps Φ ∶Sn−1→U(N) with
- Math-5646 Scalar Curvature Question [?41]: For instance, ifX =SO(n) withn≥5, then no known method can rule out metricsg ≥g on X with Sc(g) > Sc(g)
- Math-5647 Scalar Curvature Question [?54]: ExtremalityofConcaveSphericalBalls
- Math-5648 Scalar Curvature Question [?55]: 18
- Math-5649 Scalar Curvature Question [?58]: there is no apparent non-trivial bound on the width ofX = Σn−1× [−1, 1]even we assume that thesectional curvat
- Math-5650 Scalar Curvature Question [?65]: Is the regular Euclidean $3$-simplex mean-convexly extremal