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Lecture by Péter Pál Pach (Budapest University of Technology and Economics): The polynomial method and the cap set problem

Jan 07, 2019 | 02:15 PM

In this talk we will look at a new variant of the polynomial method which was first used to prove that sets avoiding 3-term arithmetic progressions in groups like Z4n (Croot, Lev and myself) and Z3n (Ellenberg and Gijswijt) are exponentially small (compared to the size of the group).
We will discuss lower and upper bounds for the size of the extremal subsets, including some recent bounds found by Elsholtz and myself. We will also mention some further applications of the method, for instance, the solution of the Erdős-Szemerédi sunflower conjecture.

Time & Location

Jan 07, 2019 | 02:15 PM

Freie Universität Berlin
Institut für Informatik
Takustr. 9
14195 Berlin
Room 005 (Ground Floor)

Freie Universität Berlin
Technische Universität Berlin
Humboldt-Universität zu Berlin
Deutsche Forschungsgemeinschaft (DFG)