In this talk, we will introduce our ongoing project on Sobolev inequalities in the context of quantum markov semigroup. We mainly focus on the study of the relations between Sobolev inequalities and other typical functional inequalities, including logarithmic Sobolev inequalities, Nash inequalities and Ultra-contractivity. The talk is based on joint work with Li Gao and Marius Junge.

报告人简介: Bang Xu is currently an Assistant Professor at Xiamen University. He received his Ph.D. from Wuhan University. His research interests lies in the field of harmonic analysis and functional analysis. He has published over ten papers in mathematics journals such as Math.Ann. and J.Funct.Anal.