报告题目 (Title)：Measure growth in compact semisimple Lie groups and the Kemperman Inverse Problem（紧半单李群中的测度增长与Kemperman逆问题）

报告人 (Speaker)：Chieu-Minh Tran（National University of Singapore）

报告时间 (Time)：2023年8月7日(周一) 15:00-16:00

报告地点 (Place)：校本部 F309

邀请人(Inviter)：席东盟、李晋、张德凯

主办部门：理学院数学系

报告摘要：Suppose G is a compact semisimple Lie group, μ is the normalized Haar measure on G, and A, A^2⊆G are measurable. We show that μ(A^2)≥min{1,2μ(A)+ημ(A)(1-2μ(A))} with the absolute constant η>0 (independent from the choice of G) quantitatively determined. This is the continuous counterpart of celebrated product theorems by Helfgott, Pyber-Szabo, and Breuillard-Green-Tao. We also show a more general result for abstractly semisimple connected compact groups and resolve the Kemperman Inverse Problem from 1964. (Joint with Jing Yifan).