报告问题 (Title)：Noncommutative logarithmic Sobolev inequalities

中文问题：非交流的对数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

报告所在 (Place)：腾讯聚会（514-885-492）

约请人(Inviter)：席东盟、李晋、张德凯、吴加勇

主理部分：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.