Mathematics
Open problems, research attempts and community review.
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-4351 Numerical invariants — Question 13.3
- Math-4352 Numerical invariants — Question 13.4
- Math-4353 Numerical invariants — Question 13.5
- Math-4354 Numerical invariants — Question 13.6
- Math-4355 Numerical invariants — Question 13.7
- Math-4356 Immersed objects — Question 14.2
- Math-4357 Immersed objects — Question 14.3
- Math-4358 Immersed objects — Question 14.5
- Math-4359 Miscellaneous — Question 15.1
- Math-4360 Miscellaneous — Question 15.2
- Math-4361 Problem 1.1 — ([188, Problem 1]) Find a non-trivial knot K with VK (t) = 1.
- Math-4362 Problem 1.2 — ([188, Problem 2]) Characterize those elements of Z[t, t−1] of the form VK(t).
- Math-4363 Problem 1.4 — (J.
- Math-4364 Problem 1.5 — (J.
- Math-4365 Problem 1.6 — (J.
- Math-4366 Problem 1.7 — (J.
- Math-4367 Problem 1.8 — (J.
- Math-4368 Problem 1.9 — (X.-S.
- Math-4369 Problem 1.12 — Categorify other knot polynomials.
- Math-4370 Problem 1.13 — (A.
- Math-4371 Problem 1.15 — (M.
- Math-4372 Problem 1.17 — (A.
- Math-4373 Problem 1.18 — (A.
- Math-4374 Conjecture 1.19 — (The volume conjecture, [198, 296]) For any knot K, 2π·lim N →∞ log|JN (K)| N = v3||S3− K||, (2) where||·||denotes th…
- Math-4375 Problem 1.20 — Justify the above arguments rigorously.
- Math-4376 Conjecture 2.1 — ([220, Problem 1.92 (N)]) Fd(ZK)/Fd+1(ZK) is torsion free for each d.
- Math-4377 Conjecture 2.2 — A(S1; Z) is torsion free.
- Math-4378 Conjecture 2.3 — (X.-S.
- Math-4379 Conjecture 2.5 — Vassiliev invariants distinguish oriented knots.
- Math-4380 Problem 2.6 — Does there exists a non-trivial oriented knot which can not b e distinguished from the trivial knot by Vassiliev inva…
- Math-4381 Conjecture 2.7 — (see [220, Problem 1.89 (B)]) For any oriented knot K, no Vassiliev invariants distinguish K from −K.
- Math-4382 Question 2.8 — (T.
- Math-4383 Problem 2.9 — (X.-S.
- Math-4384 Problem 2.10 — (N.
- Math-4385 Conjecture 2.11 — (S.
- Math-4386 Refuting random 3SAT-instances on $O(n)$ clauses (weak form)
- Math-4387 10 Lectures and 42 Open Problems — Certifying that matrices are PSD
- Math-4388 10 Lectures and 42 Open Problems — The Paley Clique Problem
- Math-4389 10 Lectures and 42 Open Problems — Maximum and minimum bisections on random regular graphs
- Math-4390 10 Lectures and 42 Open Problems — Sharp tightness of the Angular Synchronization SDP
- Math-4391 10 Lectures and 42 Open Problems — Consistency and sample complexity of Multireference Alignment
- Math-4392 Computational Diffie–Hellman problem
- Math-4393 8.4 (Schleimer) — Detecting reducible Heegaard splittings
- Math-4394 Linear collapse, binomial hypersurfaces, and the image of local-odds fibers
- Math-4395 Compatible and complete odds-ratio specifications
- Math-4396 Zero patterns, facial sets, and exact support repair in chordal models
- Math-4397 Unique minimal Markov bases, bipartite cycles, and padding monotonicity
- Math-4398 An algebraic one-mode certificate for MANOVA
- Math-4399 Exact slack lifts for Markov bases under rounded summaries
- Math-4400 Binary independence and hierarchical models in cumulant coordinates