Monthly Archives: July 2019

TYI 39 : Can a coalition of children guarantees all being in the same class?

Posted on July 25, 2019 by Gil Kalai

There is a class of children that have just finished elementary school. Now they all move from elementary school to high school and classes are reshuffled. Each child lists three friends, and the assignment of children into classes ensures that … Continue reading →

Posted in Combinatorics, Economics, Mathematics to the rescue, Test your intuition | Tagged | 3 Comments

Matan Harel, Frank Mousset, and Wojciech Samotij and the “the infamous upper tail” problem

Posted on July 23, 2019 by Gil Kalai

Let me report today on a major breakthrough in random graph theory and probabilistic combinatorics. Congratulations to Matan, Frank, and Vojtek! Artist: Heidi Buck. “Catch a Dragon by the Tail 2” ( source ) Upper tails via high moments and entropic … Continue reading →

Posted in Combinatorics, Probability | Tagged , , | 3 Comments

Isabella Novik and Hailun Zheng: Neighborly centrally symmetric spheres exist in all dimensions!

Posted on July 20, 2019 by Gil Kalai

A tweet-long summary: The cyclic polytope is wonderful and whenever we construct an analogous object we are happy. Examples: Neighborly cubic polytopes; The amplituhedron; and as of last week, the Novik-Zheng new construction of neighborly centrally symmetric spheres! At last: … Continue reading →

Posted in Combinatorics, Convexity | Tagged , | 1 Comment

Dan Romik on the Riemann zeta function

Posted on July 17, 2019 by Gil Kalai

This post, about the Riemann zeta function, which is among the most important and mysterious mathematical objects was kindly written by Dan Romik. It is related to his paper Orthogonal polynomial expansions for the Riemann xi function,  that we mentioned … Continue reading →

Posted in Combinatorics, Guest blogger, Number theory | Tagged , , , , | 4 Comments

Itai Benjamini and Jeremie Brieussel: Noise Sensitivity Meets Group Theory

Posted on July 15, 2019 by Gil Kalai

The final  version of my ICM 2018 paper Three puzzles on mathematics computation and games has been available for some time. (This proceedings’ version, unlike the arXived version has a full list of references.)  In this post I would like to … Continue reading →

Posted in Algebra, Combinatorics, Probability | Tagged , , | 1 Comment

Imre Bárány: Limit shape

Posted on July 9, 2019 by Gil Kalai

Limit shapes are fascinating objects in the interface between probability and geometry and between the discrete and the continuous. This post is kindly contributed by Imre Bárány. What is a limit shape? There are finitely many convex lattice polygons contained … Continue reading →

Posted in Combinatorics, Convexity, Geometry, Guest blogger, Probability | Tagged , | 5 Comments

Amazing: Hao Huang Proved the Sensitivity Conjecture!

Posted on July 2, 2019 by Gil Kalai

Today’s arXived amazing paper by Hao Huang Induced subgraphs of hypercubes and a proof of the Sensitivity Conjecture Contains an amazingly short and beautiful proof of a famous open problem from the theory of computing – the sensitivity conjecture posed … Continue reading →

Posted in Combinatorics, Computer Science and Optimization | Tagged , | 27 Comments