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.

Speaker Biography:Xu Zhendong graduated from Wuhan University and Franche Comt é University in France. He is currently a postdoctoral fellow at Seoul National University in South Korea, mainly engaged in functional analysis and non exchange analysis. His research work has been published in journals such as Trans. AMS, J. Funct. Anal., Math Ann.