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何伟鲲 博士:Expander graphs, random walks and sum-product phenomenon

本站小编 Free考研考试/2021-12-26


Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
Speaker: 何伟鲲 博士，KIAS
Inviter:
Title:
 Expander graphs, random walks and sum-product phenomenon
Time & Venue:
 2021.04.15 10:30-11:30 南楼N204 腾讯会议：316 783 499
Abstract:
 Ever since the notion of expander graphs came to light, mathematicians used various Cayley graphs to construct families of expander graphs. One natural construction is to take a linear group with coefficients in the integers and take its reductions modulo different integers. Recently, my coauthor Nicolas de Saxcé and myself proved that if the Zariski closure of the linear group is absolutely simple, then the family of Cayley graphs constructed in this way using modulo arbitrary integer is indeed a family of Cayley graphs. This generalizes a result of Bourgain and Varju. In this talk, I will start with the background of this problem. Then I will present the tools we developed leading to this result, namely quantitative equidistribution of random walks on the torus and sum-product estimates in matrix algebras. Finally, I will discuss some other application of these tools, in Ergodic theory and in Geometric measure theory.

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