Created in 2023, the Cours Peccot International specifically rewards young European women mathematicians, inviting them to give a series of lectures at the Collège de France.
Lisa Sauermann is the winner for 2024-2025, and will give a series of 4 lectures in February and March 2025.
A few years ago, a new polynomial method in combinatorics was introduced by Croot-Lev-Pach, and then adapted by Tao into what is now called the slice rank polynomial method. This method was developed in the context of proving upper bounds for the sizes of three-term progression free sets, in particular Ellenberg and Gijswijt used it to obtain spectacular new upper bounds for the sizes of three-term progression free subsets of F_p^n for a fixed prime p and large n. This lecture series will start by discussing this problem and related additive combinatorics problems, such as estimating the maximum possible size of a three-term progression free subset of {1,...,N} for large N. The lecture series will explain the slice rank polynomial method, and show the bounds that can be obtained via this method for three-term progression free subsets of F_p^n. Further applications of the slice rank polynomial method to other problems will also be discussed, in particular to the Erdös-Ginzburg-Ziv Problem in
