Category Archives: Combinatorics

Hardness of Approximating Vertex Cover, Polytope-Integrality-Gap, the Alswede-Kachatrian theorem, and More.

Lior Silberman asked about applications of the new Khot-Minzer-Safra 2-to-2 game theorem to hardness of approximation, and James Lee answered mentioning applications to vertex cover. Let me elaborate a little on vertex cover, and other matters. (Here is the pervious … Continue reading

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Jacob Fox, David Conlon, and Benny Sudakov: Vast Improvement of our Knowledge on Unavoidable Patterns in Words

I heard a lecture by Benny Sudakov on the remarkable paper  Tower-type bounds for unavoidable patterns in words, by David Conlon, Jacob Fox, and Benny Sudakov.  Here are the slides, and let me let the slides speak for themselves. The problem

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Subhash Khot, Dor Minzer and Muli Safra proved the 2-to-2 Games Conjecture

Update: A related blog post by Boaz Barak: Unique Games Conjecture – halfway there? The 2-to-2 Games Conjecture is a somewhat weaker form of Khot’s unique game conjecture. The paper is: Pseudorandom Sets in Grassmann Graph have Near-Perfect Expansion by Subhash Khot, Dor … Continue reading

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Interesting Times in Mathematics: Enumeration Without Numbers, Group Theory Without Groups.

Lie Theory without Groups: Enumerative Geometry and Quantization of Symplectic Resolutions Our 21th Midrasha (school) IIAS, January 7 – January 12, 2018 Jerusalem Enumerative Geometry Beyond Numbers MSRI,  January 16, 2018 to May 25, 2018 Abstract for the Midrasha

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Cody Murray and Ryan Williams’ new ACC breakthrough: Updates from Oded Goldreich’s Choices

Thanks to Irit Dinur for telling me about the following: Oded Goldreich’s recent choice is about the paper: Circuit Lower Bounds for Nondeterministic Quasi-Polytime: An Easy Witness Lemma for NP and NQP, by Corry Murray and Ryan Williams. Ryan Williams … Continue reading

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Yael Tauman Kalai’s ICM2018 Paper, My Paper, and Cryptography

Yael Tauman Kalai: Delegating Computation via No-Signaling Strategies. Ladies and Gentelmen,  Here is, exclusively for our readers, Yael Tauman Kalai’s ICM2018 paper: Delegating Computation via No-Signaling Strategies. The opportunity to present the paper arose when a week ago I attended … Continue reading

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Ilan Karpas: Frankl’s Conjecture for Large Families

Frankl’s conjecture Frankl’s conjecture is the following: Let be a finite family of finite subsets of which is closed under union, namely,  if then also . Then there exists an element which belongs to at least half the sets in . … Continue reading

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Third third of my ICM 2018 paper – Three Puzzles on Mathematics, Computation and Games. Corrections and comments welcome

Update: Here is a combined version of all three parts: Three puzzles on mathematics computations and games. Thanks for the remarks and corrections. More corrections and comments welcome. Dear all, here is the draft of the third third of my … Continue reading

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Second third of my ICM 2018 paper – Three Puzzles on Mathematics, Computation and Games. Corrections and comments welcome

Update: Here is a combined version of all three parts: Three puzzles on mathematics computations and games. Thanks for the remarks and corrections. More corrections and comments welcome. Dear all, here is the draft of the second third of my paper … Continue reading

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First third of my ICM2018 paper – Three Puzzles on Mathematics, Computation and Games. Corrections and comments welcome

Update: Here is a combined version of all three parts: Three puzzles on mathematics computations and games. Thanks for the remarks and corrections. More corrections and comments welcome. I have a very strict December 20 deadline (self-imposed, I missed the … Continue reading

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