Speaker: 王航 (华东师范大学)
Time: 2026-01-23 14:00-16:00
Location: 1410, SIMIS
Zoom Meeting ID: 818 3019 1319 Passcode: SIMIS
摘要：
In this second lecture, we examine the operator-theoretic formulation of the Mackey analogy by directly computing and comparing the K-theory of the reduced group C*-algebras for a semisimple Lie group G and its associated motion group G_0. We begin by analyzing the structure of C*(G_0) as a crossed product, utilizing the noncommutative Fourier transform to identify it with an algebra of sections of a bundle over the dual of the Lie algebra quotient. We then examine C*_r(G), particularly for complex semisimple groups. Through explicit examples, we verify that the K-theory groups for G and G_0 are isomorphic, providing a computational verification of the Connes-Kasparov ismorphism, a K-theoretic formulation of the Mackey analogy.
About Speaker:
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.
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