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Research seminar in Discrete Mathematics
On the Erdös-Ginzburg-Ziv Problem in large dimension
On the Erdös-Ginzburg-Ziv Problem in large dimension
Organizer
Benjamin Sudakov
Speaker
Lisa Sauermann
Time
Tuesday, March 26, 2024 5:05 PM - 6:15 PM
Venue
Online
Online
Zoom 787 662 9899
(BIMSA)
Abstract
The Erdös-Ginzburg-Ziv Problem is a classical extremal problem in discrete geometry. Given positive integers $m$ and $n$, the problem asks about the smallest number $s$ such that among any s points in the integer lattice $\mathbb{Z}^n$ one can find $m$ points whose centroid is again a lattice point. Despite of a lot of attention over the last 50 years, this problem is still wide open. For fixed dimension $n$, Alon and Dubiner proved that the answer grows linearly with $m$. In this talk, we discuss bounds for the opposite case, where the number $m$ is fixed and the dimension $n$ is large. Joint work with Dmitrii Zakharov.
Speaker Intro
Lisa Sauermann is a Professor at the University of Bonn. She received her PhD in mathematics from Stanford University in 2019 under the supervision of Jacob Fox. She then held post-doctoral positions at Stanford University and the Institute for Advanced Study (IAS), and spent two years as an Assistant Professor at Massachusetts Institute of Technology (MIT), before joining the University of Bonn in summer 2023. She received the Richard-Rado-Prize in 2020, the European Prize in Combinatorics in 2021, a Sloan Fellowship in 2022, and the von Kaven Award in 2023.