Author Archives: Gil Kalai

Polymath 10 post 6: The Erdos-Rado sunflower conjecture, and the Turan (4,3) problem: homological approaches.

In earlier posts I proposed a homological approach to the Erdos-Rado sunflower conjecture.  I will describe again this approach in the second part of this post. Of course, discussion of other avenues for the study of the conjecture are welcome. The purpose … Continue reading

Posted in Combinatorics, Mathematics over the Internet, Open problems, Polymath10 | Tagged , | 1 Comment

Polymath 10 Emergency Post 5: The Erdos-Szemeredi Sunflower Conjecture is Now Proven.

While slowly writing Post 5 (now planned to be Post 6) of our polymath10 project on the Erdos-Rado sunflower conjecture, the very recent proof (see this post) that cap sets have  exponentially small density has changed matters greatly! It implies … Continue reading

Posted in Combinatorics, Polymath10 | Tagged , , , | 28 Comments

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 Croot-Lev-Pach 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 , , , , , | 18 Comments

More Math from Facebook

David Conlon pointed out to two remarkable papers that appeared on the arxive: Joel Moreira solves an old problem in Ramsey’s theory. Monochromatic sums and products in . Abstract: An old question in Ramsey theory asks whether any finite coloring … Continue reading

Posted in Combinatorics, Mathematics over the Internet, Updates | Tagged , , , | 3 Comments

The Erdős Szekeres polygon problem – Solved asymptotically by Andrew Suk.

Here is the abstract of a recent paper by Andrew Suk. (I heard about it from a Facebook post by Yufei Zhao. I added a link to the original Erdős Szekeres’s paper.) Let ES(n) be the smallest integer such that … Continue reading

Posted in Combinatorics, Geometry, Updates | Tagged | 2 Comments

The Quantum Computer Puzzle @ Notices of the AMS

The Quantum Computer Puzzle My paper “the quantum computer puzzle” has just appeared in the May 2016 issue of Notices of the AMS. Here are the beautiful drawings for the paper (representing the “optimistic view” and the “pessimistic view”) by my … Continue reading

Posted in Combinatorics, Quantum, Updates | Tagged , | 4 Comments

Three Conferences: Joel Spencer, April 29-30, Courant; Joel Hass May 20-22, Berkeley, Jean Bourgain May 21-24, IAS, Princeton

Dear all, I would like to advertise three  promising-to-be wonderful mathematical conferences in the very near future. Quick TYI. See if you can guess the title and speaker for  a lecture described by  “where the mathematics of Cauchy, Fourier, Sobolev, … Continue reading

Posted in Analysis, Combinatorics, Conferences, Geometry, Updates | Tagged , , | Leave a comment

Math and Physics Activities at HUJI

Between 11-15 of September 2016 there will be a special mathematical workshop for excellent undergraduate students at the Hebrew University of Jerusalem. In parallel there will also be a workshop in physics. These workshops are aimed for second and third … Continue reading

Posted in Teaching, Updates | Tagged | Leave a comment

Stefan Steinerberger: The Ulam Sequence

This post is authored by Stefan Steinerberger. The Ulam sequence is defined by starting with 1,2 and then repeatedly adding the smallest integer that is (1) larger than the last element and (2) can be written as the sum of two … Continue reading

Posted in Guest blogger, Open problems | Tagged , | 8 Comments

TYI 26: Attaining the Maximum

(Thanks, Dani!) Given a random sequence , ******, , let . and assume that .  What is the probability that the maximum value of is attained only for a single value of ? Test your intuition: is this probability bounded … Continue reading

Posted in Combinatorics, Probability, Test your intuition | Tagged | 21 Comments