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On the cap-set problem and the slice rank polynomial method

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Sprecher: Lisa Sauermann
Veranstaltung: Dienstag, den 15. Juni 2021 16:00 - 16:50

Lisa Sauermann, mathematician at the Institute for Advanced Study (IAS) will give a lecture about "On the cap-set problem and the slice rank polynomial method".

This lecture is part of the "Multiplicities" initiative launched by the Department of Mathematics at the University of Luxembourg. Multiplicities is a broad audience seminar geared towards transversal topics whose aim is to highlight the diversity of mathematics and mathematicians. It is especially intended for PhD students, interested in widening their horizons and is supported by the PRIDE Grant “Geometry, Probability and their Synergies (GPS)”.

About the topic

In 2016, Ellenberg and Gijswijt made a breakthrough on the famous cap-set problem, which asks about the maximum size of a subset of F3n not containing a three-term arithmetic progression. They proved that any such set has size at most 2.756n. Their proof was later reformulated by Tao, introducing what is now called the slice rank polynomial method. This talk will discuss Tao's proof of the Ellenberg-Gijswijt bound for the cap-set problem, as well as further applications of Tao's slice rank polynomial method.

About the speaker

Lisa Sauermann is a member of the Computer Science and Discrete Mathematics group at the Institute for Advanced Study (IAS). Her main research interests are extremal and probabilistic combinatorics. She received her PhD in mathematics from Stanford University in Spring 2019. During the academic year 2019/2020, she was a Szegő Assistant Professor at Stanford. Starting in summer 2021, she will be an Assistant Professor at MIT.