上海大学核心数学研究所——几何与分析综合报告第40讲 紧半单李群中的测度增长与Kemperman逆问题

创建时间:  2023/08/02  龚惠英   浏览次数:   返回

报告题目 (Title):Measure growth in compact semisimple Lie groups and the Kemperman Inverse Problem

中文标题: 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).

上一条:上海大学核心数学研究所——几何与分析综合报告第41讲 SO(3,R)中小集合的测度加倍

下一条:数学学科Seminar第2435讲 PINN的失败及其隐式偏差


上海大学核心数学研究所——几何与分析综合报告第40讲 紧半单李群中的测度增长与Kemperman逆问题

创建时间:  2023/08/02  龚惠英   浏览次数:   返回

报告题目 (Title):Measure growth in compact semisimple Lie groups and the Kemperman Inverse Problem

中文标题: 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).

上一条:上海大学核心数学研究所——几何与分析综合报告第41讲 SO(3,R)中小集合的测度加倍

下一条:数学学科Seminar第2435讲 PINN的失败及其隐式偏差