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Combinatorics: Noam Lifshitz | Einstein Institute of Mathematics

Combinatorics: Noam Lifshitz

Date: 
Mon, 28/11/202211:00-13:00
Location: 
Ross 63

Title: Product free sets in groups


Abstract:

A subset of a group G is said to be product free if the product of each two elements inside it is outside of the set. In 1985 Babai and Sos considered the problem of determining the largest product free sets in the alternating group and in finite simple groups in general. We show the complete solution of this problem when $n$ is sufficiently large. We also discuss progress on the corresponding problems for compact Lie groups. Our methods involve a variety of fields. These include:
-combinatorial ideas*
-representation theoretic ideas**
-analytic ideas***
-and ideas from differential geometry****.    
Based on joint works with Ellis, Keevash, Kindler and Minzer 
*The junta method and the stability method
**Trace method/Quasirandomness and the structure of the isotypical component
***Hypercontractivity: Using L_p norms to get more information
****Using  Ricci curvature to obtain hypercontractivity