报告题目 (Title)：Noncommutative logarithmic Sobolev inequalities

中文标题：非交换的对数Sobolev不等式

报告人 (Speaker)：焦勇 教授（中南大学）

报告时间 (Time)：2024年4月10日(周三) 10:00

报告地点 (Place)：腾讯会议（514-885-492）

邀请人(Inviter)：席东盟、李晋、张德凯、吴加勇

主办部门：理学院数学系

报告摘要：We show that the logarithmic Sobolev inequality holds for an arbitrary hypercontractive semigroup acting on a noncommutative probability space. Particularly, we can recover the p-logarithmic Sobolev inequality whenever the Riesz transform is bounded. Our inequality applies to numerous concrete cases, including Poisson semigroups for free groups, the Ornstein-Uhlenbeck semigroup for mixed Q-gaussian von Neumann algebras, the free product for Ornstein-Uhlenbeck semigroups etc. This provides a unified abstract approach to logarithmic Sobolev inequalities in noncommutative setting.