On the Erds-Ginzburg-Ziv Problem in large dimension | Research seminar in Discrete Mathematics

Abstract

The Erds-Ginzburg-Ziv Problem is a classical extremal problem in discrete geometry. Givenpositive integers m and n, the problem asks about the smallest number s such that among any spoints in the integer lattice Z" one can find m points whose centroid is again a lattice point. Despiteof a lot of attention over the last 50 years, this problem is stil wide open. For fixed dimension nAlon and Dubiner proved that the answer grows linearly with m. In this talk, we discuss bounds forthe opposite case, where the number m is fixed and the dimension n is large. Joint work withDmitrii Zakharov.

Speaker Intro

Lisa Sauermann is a Professor at the University of Bonn. She received her PhD in mathematicsfrom Stanford University in 2019 under the supervision of Jacob Fox. She then held post-doctoralpositions at Stanford University and the Institute for Advanced Study (lAS), and spent two years asan Assistant Professor at Massachusetts Institute of Technology (MlT), before joining the Universityof Bonn in summer 2023, She received the Richard-Rado-Prize in 2020. the European Prize inCombinatorics in 2021, a Sloan Fellowship in 2022, and the von Kaven Award in 2023.