Tags » Polynomial Method

Polynomial Method Workshop

The workshop on the  “polynomial method” will take place at the Hebrew University of Jerusalem on Monday Dec 26 and Tuesday Dec 27. The event is organized by Jordan Ellenberg and Gil Kalai. 183 more words


Notes on the "slice rank" of tensors

In the previous blog post, one of us (Terry) implicitly introduced a notion of rank for tensors which is a little different from the usual notion of tensor rank, and which (following… 3,914 more words


Applications of Alon-Furedi to finite geometry

In a previous post I discussed how the Alon-Furedi theorem serves as a common generalisation of the results of Schwartz, DeMillo, Lipton and Zippel. Here I will show some nice applications of this theorem to finite geometry (reference: Section 6 of… 973 more words


A symmetric formulation of the Croot-Lev-Pach-Ellenberg-Gijswijt capset bound

A capset in the vector space over the finite field of three elements is a subset of that does not contain any lines , where and . 1,355 more words


Ellenberg's announcement of a solution to the cap-set problem

Jordan Ellenberg has just announced a resolution of the “cap problem” using techniques of Croot, Lev and Pach, in a self-contained three-page paper. This is a quite unexpected development for a long-standing open problem in the core of additive combinatorics. 787 more words


The Ellenberg-Gijswijt bound on cap sets

Four days back Jordan Ellenberg posted the following on his blog:

Briefly:  it seems to me that the idea of the Croot-Lev-Pach paper I posted about yesterday…

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Croot-Lev-Pach on AP-free sets in (Z/4Z)^n

As you know I love the affine cap problem:  how big can a subset of (Z/3Z)^n be that contains no three elements summing to 0 — or, in other words, that contains no 3-term arithmetic progression?   840 more words