UVic Distinguished Women Scholar Award and Lectures - Lisa Sauermann
Lisa Sauermann from MIT has received the UVic Distinguished Women Scholars Award and will give a series of lectures on November 16, 17 and 19 on "The slice rank polynomial method and applications".
Speaker: Lisa Sauermann, MIT
Dates and time: 16, 17, 19 Nov 2021, 11:30am - 12:30pm
Location: In a classroom TBA and Zoom
The lectures will be available via zoom and also will be projected live in a classroom. Please register (for both the zoom sessions and the classroom session) here:https://uvic.zoom.us/meeting/register/tZ0qdeutqTwoGtQF4_F8zJLxOovazzLI7APa
In 2016, Tao introduced the slice rank polynomial method as a reformulation of a technique that first appeared in work of Croot, Lev and Pach, and was the basis of a breakthrough of Ellenberg and Gijswijt on the upper bound for the famous cap-set problem. The cap-set problem asks about the maximum size of a subset of F_3^n not containing a three-term arithmetic progression. In this series of three lectures, we will discuss the slice rank polynomial method, various applications, and some of its limitations.
In the first lecture, we will give some background and show (following Tao) how the slice rank polynomial method can be used to show the Ellenberg-Gijswijt bound for the cap-set problem. The second lecture will discuss more applications, in particular a result of Naslund and Sawin on the so-called Erdös-Szemeredi sunflower problem (which is a problem in extremal set theory), as well as an upper bound for the maximum size of a subset of F_p^n that does not contain p distinct vectors summng to zero. The problem of determining the maximum size of such a subset is closely related to the Erdös-Ginzburg-Ziv problem in discrete geometry. In the third lecture, we will continue to discuss this problem, showing a much better upper bound by combining the slice rank polynomial method with with additional combinatorial ideas.
Lisa also says: I will do my best to make the lecture accessible to final year undergraduates (the first two lectures should definitely be accessible; the third might be a little bit more technical, but I hope that it will also still be accessible).
Lisa is the recipient of a UVic DWS award. The Distinguished Women Scholars (DWS) Awards and Lecture Series were established by the Provost to highlight and honour outstanding research and creative achievements by female-identifying scholars. The purpose of these awards is to celebrate, recognize and share the impact of outstanding research and creative achievements by women at any stage of their careers.