Speaker:    

Dr. Chieu-Minh Tran，University of Notre Dame
Inviter:      
Title:
    The Kemperman inverse problem
Time & Venue:
    2021.12.29 10:30-11:30 南楼N204室 Zoom会议：412 019 4771 密码：mcm1234
Abstract:
    

Let $G$ be a connected locally compact group with a left Haar measure $\mu$, and let $A,B \subseteq G$ be nonempty and compact. Assume further that $G$ is unimodular, i.e., $\mu$ is also the right Haar measure; this holds, e.g., when $G$ is compact, a nilpotent Lie group, or a semisimple Lie group. In 1964, Kemperman showed that
$$ \mu(AB) \geq \min \{\mu(A)+\mu(B), \mu(G)\} .$$
The Kemperman inverse problem (proposed by Griesmer, Kemperman, and Tao) asks when the equality happens or nearly happens. I will discuss the recent solution of this problem, highlighting the roles played by model theory and descriptive set theory. (Joint with Jinpeng An, Yifan Jing, and Ruixiang Zhang)
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