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-5701 Worst cases for LLL on ideal lattices
- Math-5702 An algebraic LLL algorithm
- Math-5703 Ideal-lattice pseudorandom functions
- Math-5704 Converting between divisor-class and infrastructure discrete logarithms
- Math-5705 Relaxation time of Metropolis chains on Cayley graphs
- Math-5706 Spectral gap of a Bayesian graph Laplacian
- Math-5707 Excursion counts in a random Eulerian circuit on a complete graph
- Math-5708 Largest-city growth at alpha=1
- Math-5709 Scaling limit of random recursive square subdivision
- Math-5710 Random lattice embeddings with exponential intersection tails
- Math-5711 Three-dimensional sphere packing from a planar height function
- Math-5712 Mutually avoiding competing random walks
- Math-5713 Exponential upper bound for linear-time graph covering
- Math-5714 Sublaminations and superlaminations — Question 6.2
- Math-5715 Problem 1.16 — (E.
- Math-5716 Problem 1.22 — (H.
- Math-5717 Question 2.4 — (T.
- Math-5718 Problem 2.14 — (M.
- Math-5719 Conjecture 2.21 — (A.
- Math-5720 Problem 3.17 — Find a topological construction of the 2-loop polynomial P θ K.
- Math-5721 Problem 4.2 — (J.
- Math-5722 Problem 4.4 — (J.
- Math-5723 Problem 4.14 — (J.
- Math-5724 Conjecture 4.15 — (J.
- Math-5725 Problem 5.2 — Describe (the number of) representations of a knot quandle t o a fixed connected quandle of finite order, say, by usi…
- Math-5726 Problem 5.11 — (C.
- Math-5727 Conjecture 5.12 — (R.
- Math-5728 Problem 6.5 — (S.J.
- Math-5729 Conjecture 7.5 — For non-vanishing $\tau_r^G(M)$, the absolute value $|\tau_r^G(M)|$ depends only on the fundamental group $\pi_1(M)$.
- Math-5730 Problem 7.13 — (H.
- Math-5731 Problem 7.18 — (S.
- Math-5732 Problem 7.19 — (S.
- Math-5733 Problem 7.20 — (S.
- Math-5734 Problem 7.21 — (S.
- Math-5735 Problem 7.24 — (S.
- Math-5736 Problem 8.6 — (V.
- Math-5737 Problem 9.4 — (Y.
- Math-5738 Problem 9.5 — (Y.
- Math-5739 Problem 9.9 — (N.
- Math-5740 Problem 9.11 — (N.
- Math-5741 Problem 10.1 — Can the Casson invariant of an integral homology 3-sphere M be characterized by the signature of a certain 4-manifold…
- Math-5742 Problem 10.4 — (M.
- Math-5743 Question 10.21 — (F.
- Math-5744 Problem 12.3 — (H.R.
- Math-5745 Conjecture 12.4 — (3-move conjecture, Y.
- Math-5746 Conjecture 12.5 — (Y.
- Math-5747 Problem 12.6 — Find a new proof of the existence of a universal Vassiliev in- variant of knots, presenting them by KTG’s and their o…
- Math-5748 Problem 12.11 — (D.
- Math-5749 Problem 12.14 — (N.
- Math-5750 Problem 12.21 — (Y.