汇报标题 (Title)：A nonabelian Brunn-Minkowski inequality
中文标题: 非互换的Brunn-Minkowski不等式
汇报人 (Speaker)：张瑞祥（加州大学伯克利分校）
汇报功夫 (Time)：2023年6月24日(周六) 10:00-11:00
汇报地址 (Place)：校本部F309
约请人(Inviter)：席东盟、李晋、张德凯
主办部门：理学院数学系
汇报提要：The celebrated Brunn-Minkowski inequality states that for compact subsets X and Y of R^d, 〖m(X+Y)〗^(1/d)≥〖m(X)〗^(1/d)+〖m(Y)〗^(1/d)where m(?) is the Lebesgue measure. We will introduce a conjecture generalizing this inequality to every locally compact group where the exponent is believed to be sharp. In a joint work with Yifan Jing and Chieu-Minh Tran, we prove this conjecture for a large class of groups (including e.g. all real linear algebraic groups). We also prove that the general conjecture will follow from the simple Lie group case. For those groups where we do not know the conjecture yet (one typical example being the universal covering of SL_2 （R）, we also obtain partial results. In this talk I will discuss this inequality and explain important ingredients, old and new, in our proof.
