Category Archives: Combinatorics

AviFest, AviStories and Amazing Cash Prizes.

  Ladies and gentlemen,  a workshop in Princeton in honor of Avi Wigderson’s 60th birthday  is coming on October. It will take place at Princeton on October 5-8 2016 right before FOCS 2016.  Don’t miss the event ! Attendance is free but … Continue reading

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

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 , | 5 Comments

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 , , , | 35 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 , , , , , | 19 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

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

A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24

Maryna Viazovska The news Maryna Viazovska has solved the densest packing problem in dimension eight! Subsequently, Maryna Viazovska with Henry Cohn, Steve Miller, Abhinav Kumar, and Danilo Radchenko solved the densest packing problem in 24 dimensions! Here are the links to … Continue reading

Posted in Combinatorics, Geometry, Updates | Tagged , , , , , , | 15 Comments