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Improved Covering Results and Intersection Theorems in Symmetric Groups via Hypercontractivity

Hausdorff Center for Mathematics via YouTube

Overview

Explore advanced mathematical concepts in this 47-minute lecture focusing on two key results concerning symmetric groups. Delve into the characterization of subsets A of An whose square A^2 covers the entire alternating group An, discovering how conjugacy classes with density of at least exp(-n^{2/5} - ε) lead to An = A^2 - an improvement on Larsen and Shalev's previous findings. Examine the Erdős-Sós forbidden intersection problem for permutation families, learning how non-(t-1)-intersecting families with t ≤ √n/log(n) have a maximal size of (n-t)!. Understand how both results connect to independent sets in normal Cayley graphs over symmetric groups, utilizing hypercontractive inequalities for global functions developed by Keller, Lifshitz, Marcus, Keevash, and others.

Syllabus

Ohad Sheinfeld: Improved Covering Results & Intersection Theorems in Symmetric Groups

Taught by

Hausdorff Center for Mathematics

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