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 To cheer you up in difficult times 12: Asaf Ferber and David Conlon found new lower bounds for diagonal Ramsey numbers
 Alef Corner: Math Collaboration
 Alef’s Corner: Math Collaboration 2
 To cheer you up in difficult times 11: Immortal Songs by Sabine Hossenfelder and by Tom Lehrer
 To cheer you up in difficult times 10: Noam Elkies’ Piano Improvisations and more
 Quantum Matters
 To cheer you up in difficult times 9: Alexey Pokrovskiy proved that Rota’s Basis Conjecture holds asymptotically
 To Cheer you up in Difficult Times 8: Nathan Keller and Ohad Klein Proved Tomaszewski’s Conjecture on Randomly Signed Sums
 Noam Lifshitz: A new hypercontractivity inequality — The proof!
Top Posts & Pages
 To cheer you up in difficult times 12: Asaf Ferber and David Conlon found new lower bounds for diagonal Ramsey numbers
 TYI 30: Expected number of Dice throws
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 TYI44: "What Then, To Raise an Old Question, is Mathematics?"
 Quantum Matters
 Game Theory 2020
 Are Natural Mathematical Problems Bad Problems?
 A sensation in the morning news  Yaroslav Shitov: Counterexamples to Hedetniemi's conjecture.
 Amazing: Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John Wright, and Henry Yuen proved that MIP* = RE and thus disproved Connes 1976 Embedding Conjecture, and provided a negative answer to Tsirelson's problem.
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Tag Archives: Cap sets
Mind Boggling: Following the work of Croot, Lev, and Pach, Jordan Ellenberg settled the cap set problem!
A quote from a recent post from Jordan Ellenberg‘s blog Quomodocumque: Briefly: it seems to me that the idea of the CrootLevPach paper I posted about yesterday (GK: see also my last post) can indeed be used to give a new bound … Continue reading
Posted in Combinatorics, Open problems, Updates
Tagged Cap sets, Dion Gijswijt, Ernie Croot, Jordan Ellenberg, Peter Pach, Seva Lev.
24 Comments
Cap Sets, Sunflowers, and Matrix Multiplication
This post follows a recent paper On sunflowers and matrix multiplication by Noga Alon, Amir Spilka, and Christopher Umens (ASU11) which rely on an earlier paper Grouptheoretic algorithms for matrix multiplication, by Henry Cohn, Robert Kleinberg, Balasz Szegedy, and Christopher Umans (CKSU05), … Continue reading
The CapSet Problem and FranklRodl Theorem (C)
Update: This is a third of three posts (part I, part II) proposing some extensions of the cap set problem and some connections with the Frankl Rodl theorem. Here is a post presenting the problem on Terry Tao’s blog (March 2007). Here … Continue reading
Around the CapSet problem (B)
Part B: Finding special cap sets This is a second part in a 3part series about variations on the cap set problem that I studied with Roy Meshulam. (The first post is here.) I will use here a different notation than in part … Continue reading
An Open Discussion and Polls: Around Roth’s Theorem
Suppose that is a subset of of maximum cardinality not containing an arithmetic progression of length 3. Let . How does behave? We do not really know. Will it help talking about it? Can we somehow look beyond the horizon and try to guess what … Continue reading
Posted in Combinatorics, Open discussion, Open problems
Tagged Cap sets, polymath1, Roth's theorem, Szemeredi's theorem
28 Comments
FranklRodl’s Theorem and Variations on the Cap Set Problem: A Recent Research Project with Roy Meshulam (A)
Voita Rodl I would like to tell you about a research project in progress with Roy Meshulam. (We started it in the summer, but then moved to other things; so far there are interesting insights, and perhaps problems, but not substantial … Continue reading
Posted in Combinatorics, Open problems
Tagged Cap sets, Extremal combinatorics, Intersection theorems, polymath1
9 Comments