Analysis on Lie groups and abstract harmonic analysis are two closely related fields. These two fields were studied together in the original works of Godement, Segal and Gelfand, and were diverted later on. However, recent developments indicated that it is important to combine the concrete Lie group analysis and the abstract Banach algebra techniques, in order to develop some systematic theory for representations of infinite dimensional Lie groups. In particular, the striking advancements for the branching problems made by, among many others, T. Kobayashi, B. Sun and C.-B. Zhu call for a new formulation in the setting of representations in Banach spaces. 

This workshop intends to bring some leading Chinese and overseas experts on these two subjects to TSIMF, and to offer young Chinese mathematicians an opportunity to meet with the experts. We shall focus on the following topics and related problems. 

(1) Dirac cohomology of representations of semisimple Lie groups and its application to branching rules, realization of quaternionic representations and their application to classical quaternionic analysis. 

(2) Positive definite functions on Lie groups and their relation with probability theory and amenability problem in Banach algebras.