报告人：曾强 （Qiang Zeng), Northwestern University, USA
Free probability was introduced by D. Voiculescu in 1980s with the motivation to study free group factors. Since then it has been developed to a subject of independent study, with many connections to functional analysis, combinatorics and probability. Nowadays it is an active research area with some major problems still open.
This is an introductory mini-course on free probability theory. We will start with the motivation and basic concepts in the subject. Then we will mainly focus on the analytical side of the theory. In particular, we will mention some connections to random matrices. The mini-course will also touch some aspects of the theory of operator algebras (C*-algebras and von Neumann algebras), which is the foundation of free Probability. Along the way, we will see a mixture of notions and techniques from probability, analysis and algebra. For example, the fundamental notion of freeness can be regarded as a strong form of independence, but many examples involves analytical and Algebraic techniques.
The lectures are intended to be accessible to advanced undergraduate students and beyond who know basic probability theory and functional analysis. No background in operator algebras will be assumed.