**Speaker**: Hang Wang (ECNU)

**Abstract**: Let G be a connected, real semisimple Lie group, and K a maximal compact subgroup. For a discrete subgroup Γ in G, we have the locally symmetric space X = Γ\G/K. Such spaces appear in many places in mathematics and include, for example, all hyperbolic manifolds. Our research was strongly motivated by the theory of trace formulas that relate geometry and representation theory. If X is smooth and compact, then Atiyah-Singer index theory is a source of useful and computable invariants of X. One then also has the higher index, with values in the K-theory of the C∗-algebra of Γ. In many relevant cases X is noncompact, but still has finite volume. Then Moscovici showed in the 1980s that a relevant index of Dirac operators on X can still be defined, and Barbasch and Moscovici computed this index in terms of group-theoretic information, making use of the Selberg trace formula. With Hao Guo and Peter Hochs, we construct a K-theoretic index, from which Moscovici’s index, and the individual terms in Barbasch and Moscovici’s index theorem, can be extracted and computed.

**Time**: 14:30-15:30, Thursday, September 5, 2024

**Location**: Room 1610, 16th Floor, Block A, No. 657 Songhu Road, Yangpu District, Shanghai

**Zoom Meeting No.:** 423 317 8953

Password: SIMIS

**Introduction to Professor Hang Wang**

Professor Hang Wang is the chairwoman of the Department of Fundamental Mathematics at the School of Mathematical Sciences, East China Normal University. She received her B.S. from Fudan University in 2006, her Ph.D. from Vanderbilt University in 2011 under the supervision of Gennadi Kasparov, and her postdoctoral fellowship at the Yau Mathematical Sciences Center at Tsinghua University from 2011 to 2013. She worked at the University of Adelaide from 2013 to 2017. In 2016, Professor Wang was awarded the Discovery Early Career Researcher Award and shortly after was selected for Thousand Youth Talents Program. In 2019, she was recognized with the Shanghai Rising-Star Program. Professor Wang’s research interests involve noncommutative geometry and operator algebras with applications in topology, geometry and representation theory. She has published in top-tier mathematical journals such as the Journal of Differential Geometry, Advances in Mathematics, and the Proceedings of the London Mathematical Society.