报告摘要：

Abstract: We introduce the pro-tensor network, a categorification of the tensor network, as a fully rigorous yet graphically transparent framework for studying the collection of many many-body theories, which we dub many-many-body theory. We provide a comprehensive toolbox for the graphical calculations using pro-tensor networks. As applications, we recover the Levin-Wen model as a "uniform" pro-tensor network and generalize a result of Kitaev and Kong by characterizing particles as modules over promonads. One can also interpret the string-net pro-tensor network as the space of symmetric tensor networks, thus our framework also applies to the study of generalized symmetry and topological holography. Notably, our generalization dispenses with the assumptions of semisimplicity, finiteness, and rigidity, potentially facilitating the exploration of many-body physics beyond these constraints.

个人简介：Tian Lan is an Assistant Professor at The Chinese University of Hong Kong. His research explores topological phases of matter, generalized symmetries, and category theory, aiming to build rigorous mathematical frameworks for understanding quantum many-body systems.

邀请人：周毅 yizhou@iphy.ac.cn