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Aleksa Stankovic: Upper bounds on the size of subsets in F_3^n without three-term arithmetic progressions

Time: Fri 2020-04-03 13.00 - 14.00

Location: Zoom meeting ID 206 867 499

Participating: Aleksa Stankovic

This seminar will be helt via Zoom, the meeting ID is 287 089 562.


A celebrated result of Ellenberg-Gijswit building upon the application of polynomial method in the work of Croot-Lev-Pach shows that, given some F_q, there is a constant c<q such that any subset of F_q^n larger than c^n must contain three-term arithmetic progression, i.e. three distinct elements a,b,c such that b-a=c-b. The goal of this talk will be to give a proof of this result in F_3^n, and discuss some related questions in additive combinatorics (e.g. theorems of Roth and Szemerédi).

I will not assume any previous knowledge on the topic, and therefore the talk should be accessible to audience with diverse mathematical backgrounds. The main objects of interest in the talk will be polynomials.