Category Archives: Combinatorics

Attila Por’s Universality Result for Tverberg Partitions

In this post  I would like to tell you about three papers and three theorems. I am thankful to Moshe White and Imre Barany for helpful discussions. a) Universality of vector sequences and universality of Tverberg partitions, by Attila Por; Theorem … Continue reading

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Henry Cohn, Abhinav Kumar, Stephen D. Miller, Danylo Radchenko, and Maryna Viazovska: Universal optimality of the E8 and Leech lattices and interpolation formulas

Henry Cohn A follow up paper on the tight bounds for sphere packings in eight and 24 dimensions. (Thanks, again, Steve, for letting me know.) For the 2016 breakthroughs see this post, this post of John Baez, this article by Erica Klarreich on … Continue reading

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Extremal Combinatorics V: POSETS

This is the remaining post V on partially ordered sets of my series on extremal combinatorics (I,II,III,IV,VI).  We will talk here about POSETS – partially ordered sets. The study of order is very important in many areas of mathematics starting … Continue reading

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Konstantin Tikhomirov: The Probability that a Bernoulli Matrix is Singular

Konstantin Tikhomirov An old problem in combinatorial random matrix theory is cracked! Singularity of random Bernoulli matrices by Konstantin Tikhomirov Abstract: For each , let be an n×n random matrix with independent ±1 entries. We show that P( is singular}=, … Continue reading

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Jean

Jean Bourgain and Joram Lindenstrauss. I was very sad to hear that Jean Bourgain, among the greatest mathematicians of our time, and a dear friend, passed away.  I first met Jean about forty years ago and later we  became friends … Continue reading

Posted in Algebra and Number Theory, Analysis, Combinatorics, Computer Science and Optimization, Convexity, Obituary | Tagged | 4 Comments

Amazing: Karim Adiprasito proved the g-conjecture for spheres!

Karim in his youth with a fan Congratulations, Karim! Update: Here is the link to the paper From the arXive, Dec 26, 2018. (Link will be added tomorrow.) COMBINATORIAL LEFSCHETZ THEOREMS BEYOND POSITIVITY by Karim Adiprasito Abstract: Consider a simplicial complex … Continue reading

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ICM 2018 Rio (4): Huh; Balog & Morris; Wormald

  This is my fourth report from ICM2018. (I plan one more.)  As I already mentioned, Combinatorics  was very nicely represented at ICM2018.  The combinatorics session itself was great, and there were quite a few other sessions and other lectures … Continue reading

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Nima Anari, Kuikui Liu, Shayan Oveis Gharan, and Cynthia Vinzant Solved the Mihail-Vazirani Conjecture for Matroids!

  Milena Mihail and Umesh Vazirani I thank Nati Linial, Dan Spielman and Karim Adiprasito for sharing the news with me. The Mihail-Vazirani conjecture for matroids and Feder-Mihail’s theorem Consider a collection of vectors. A basis is a subset of … Continue reading

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Igor Pak will give the 2018 Erdős Lectures

  Next week Igor Pak will give the 2018 Erdős Lectures (delayed from June) Here is the poster   Combinatorics — Erdos lecture: Igor Pak (UCLA) “Counting linear extensions” Monday December 10  11:00-13:00 Location:  IIAS Hall 130, Feldman building,  Givat Ram     … Continue reading

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PCP fest, Tel Aviv University, 18-20 December 2018

Conference web site The study of Probabilistically Checkable Proofs, starting with the discovery of the PCP Theorem, is a cornerstone of modern computer science, with impact on complexity theory, algorithms, and cryptography. Born as a purely theoretical notion, mostly used … Continue reading

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