Category Archives: Combinatorics

Looking Again at Erdős’ Discrepancy Problem

Over Gowers’s blog Tim and I will make an attempt to revisit polymath5. Last Autumn I prepared three posts on the problems and we decided to launch them now. The first post is here. Here is a related MathOverflow question. … Continue reading

Posted in Combinatorics, Mathematics over the Internet, Open problems | 2 Comments

Tokyo, Kyoto, and Nagoya

Near Nagoya: Firework festival; Kyoto: with Gunter Ziegler; with Takayuki Hibi, Hibi, Marge Bayer, Curtis Green and Richard Stanly; Tokyo: Peter Frankl; crowded crossing. Added later: Mazi and I at the same restaurant taken by Stanley. I just returned from … Continue reading

Posted in Combinatorics, Conferences, Convex polytopes | Tagged , , , | 2 Comments

Celebrations in Sweden and Norway

Celebrations for Endre, Jean and Terry Anders Bjorner presents the 2012 Crafoord Prize in Mathematics  I am in Sweden for two weeks to work with colleagues and to take part in two celebrations. Jean Bourgain and Terence Tao are the 2012 laureates … Continue reading

Posted in Academics, Combinatorics, Conferences, Updates | Tagged , , | 3 Comments

Galvin’s Proof of Dinitz’s Conjecture

Dinitz’ conjecture The following theorem was conjectured by Jeff Dinitz in 1979 and proved by Fred Galvin in 1994: Theorem: Consider an n by n square table such that in each cell (i,j) you have a set with n or more elements. … Continue reading

Posted in Combinatorics, Games | 4 Comments

Fractional Sylvester-Gallai

Avi Wigderson was in town and gave a beautiful talk about an extension of Sylvester-Gallai theorem. Here is a link to the paper: Rank bounds for design matrices with applications to combinatorial geometry and locally correctable codes by Boaz Barak, Zeev … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Geometry | Tagged , , , | 4 Comments

Ryan O’Donnell: Analysis of Boolean Function

Ryan O’Donnell has begun writing a book about Fourier analysis of Boolean functions and  he serializes it on a blog entiled Analysis of Boolean Function.  New sections appear on Mondays, Wednesdays, and Fridays. Besides covering the basic theory, Ryan intends to describe applications … Continue reading

Posted in Combinatorics, Computer Science and Optimization | Tagged , , | 1 Comment

Cup 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 Group-theoretic algorithms for matrix multiplication, by Henry Cohn, Robert Kleinberg, Balasz Szegedy, and Christopher Umans (CKSU05), … Continue reading

Posted in Combinatorics, Computer Science and Optimization, Open problems | Tagged , , , , , , | 1 Comment

High Dimensional Expanders: Introduction I

Alex Lubotzky and I  are running together a year long course at HU on High Dimensional Expanders. High dimensional expanders are simplical (and more general) cell complexes which generalize expander graphs. The course is taking place in Room 110 of the mathematics building on … Continue reading

Posted in Combinatorics, Teaching | 4 Comments

Noise Sensitivity and Percolation. Lecture Notes by Christophe Garban and Jeff Steif

Lectures on noise sensitivity and percolation is a new beautiful monograph by Christophe Garban and Jeff Steif. (Some related posts on this blog: 1, 2, 3, 4, 5)

Posted in Combinatorics, Probability | Tagged , , , , | Leave a comment

Alantha Newman and Alexandar Nikolov Disprove Beck’s 3-Permutations Conjecture

Alantha Newman and Alexandar Nikolov disproved a few months ago one of the most famous and frustrating open problem in discrepancy theory: Beck’s 3-permutations conjecture. Their paper  A counterexample to Beck’s conjecture on the discrepancy of three permutations is already on … Continue reading

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