We establish $L_p$-Poincar\'{e}-type inequalities for ergodic quantum Markov semigroups on finite von Neumann algebras, derived directly from the $L_2$-Poincar\'{e} inequality (PI) or from the mordified logarithmic Sobolev inequality (MLSI). Crucially, we obtain the asymptotic behaviors of best constants on $L_p$-Poincar\'{e}-type inequalities: $O(\sqrt{p})$ under the MLSI, while $O(p)$ under the PI, as $p\rightarrow\infty$. Applications encompass broad classes of ergodic quantum Markov semigroups, including but not limited to those on quantum tori, mixed $q$-Gaussian algebras, group von Neumann algebras, and compact quantum groups of Kac-type.
报告人简介：徐振东，毕业于糖心视频
与法国Franche-Comté大学，现在韩国Seoul National University做博士后，主要从事泛函分析与非交换分析方向的工作，研究工作发表于在Trans. AMS, J. Funct. Anal. ,Math Ann.等杂志。
