C*-algebras are algebras of bounded linear operators on Hilbert spaces. Originally introduced as a mathematical foundation for quantum physics, these structures turn out to be interesting on their own right and exhibit a rich interplay with several other mathematical disciplines. Indeed, as I will explain, several key ideas which were initially developed to classify C*-algebras also lead to classification results for topological dynamical systems. At the same time, it was discovered recently that all C*-algebras which have been classified arise from dynamics in a precise sense. Surprisingly, this circle of ideas also leads to new constructions of groups which answered several open questions in group theory.

报告人简介：Xin Li works at the University of Glasgow as the Chair of Mathematical Analysis. His research interests include operator algebras, topological dynamics and group theory. He published papers in journals such as Invent. Math., J. Eur. Math. Soc., Amer. J. Math., Math. Ann., Comm. Math. Phys. or Adv. Math.