# "The card game SET and three-term arithmetic progressions". Hirzebruch lecture by Lisa Sauermann on Monday, 4 November 2024, University Club Bonn

Starting from the popular card game SET, we will look at questions concerning the maximum possible size of sets without three-term progressions in various different mathematical settings (namely, subsets of the numbers from 1 to some number N, and subsets of so-called vector spaces over finite fields). These are fundamental questions in additive combinatorics, with connections to several other mathematical areas. We will discuss what is known about these questions, as well as some related problems.

**Lisa Sauermann **joined the University of Bonn as a Hausdorff Chair in 2023. She completed her PhD in 2019 at Stanford University under the supervision of Jacob Fox, and then spent one more year at Stanford University as a Szegö Assistant Professor. After one year as a member at the Institute of Advanced Study, she was an Assistant Professor at the Massachusetts Institute of Technology (MIT) for two years from 2021 to 2023. She was awarded the Richard Rado Prize in 2020, the European Prize in Combinatorics in 2021 and the von Kaven Award in 2023. She also received a Sloan Fellowship in 2022 and a DFG Heisenberg Professorship in 2023. In high school, she won 4 gold medals and one silver medal in the International Mathematical Olympiad.

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