Recent Comments

Recent Posts
 Peter Cameron: Doing research
 To cheer you up in difficult times 18: Beautiful drawings by Neta Kalai for my book: “Gina Says”
 Amazing: Simpler and more general proofs for the gtheorem by Stavros Argyrios Papadakis and Vasiliki Petrotou, and by Karim Adiprasito, Stavros Argyrios Papadakis, and Vasiliki Petrotou.
 Igor Pak: What if they are all wrong?
 To cheer you up in difficult times 17: Amazing! The ErdősFaberLovász conjecture (for large n) was proved by Dong Yeap Kang, Tom Kelly, Daniela Kühn, Abhishek Methuku, and Deryk Osthus!
 Open problem session of HUJICOMBSEM: Problem #5, Gil Kalai – the 3ᵈ problem
 To cheer you up in difficult times 16: Optimism, two quotes
 The Argument Against Quantum Computers – A Very Short Introduction
 Open problem session of HUJICOMBSEM: Problem #4, Eitan Bachmat: Weighted Statistics for Permutations
Top Posts & Pages
 Peter Cameron: Doing research
 TYI 30: Expected number of Dice throws
 Amazing: Simpler and more general proofs for the gtheorem by Stavros Argyrios Papadakis and Vasiliki Petrotou, and by Karim Adiprasito, Stavros Argyrios Papadakis, and Vasiliki Petrotou.
 Igor Pak: What if they are all wrong?
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 The Argument Against Quantum Computers  A Very Short Introduction
 Chomskian Linguistics
 Dan Romik on the Riemann zeta function
 To cheer you up in difficult times 18: Beautiful drawings by Neta Kalai for my book: "Gina Says"
RSS
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.
25 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
29 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
10 Comments