Speaker: 王航 (华东师范大学)
Time: 2026-01-16 16:00-17:00
Location: 1410, SIMIS
Zoom Meeting ID: 885 0318 2392 Passcode: SIMIS
Abstract:
In the 1970s, Mackey proposed an approach to the representation theory of semisimple Lie groups that relates their tempered representations to the unitary representations of the associated motion groups, defined as crossed products of a maximal compact subgroup K acting on the vector space (\mathfrak g/\mathfrak k); this “Mackey analogy” predicts a close correspondence between these two representation theories. For a general reductive group, the reduced group C*-algebra provides an operator-theoretic model for the tempered dual, and its K-theory yields a robust topological invariant capturing essential structural information. This K-theory is computable via the Connes–Kasparov isomorphism, which identifies the K-theory of the reduced C*-algebra of an almost connected group with the representation ring of its maximal compact subgroup, constituting a central result in noncommutative geometry and a verified case of the Baum–Connes conjecture. From a geometric viewpoint, the Mackey analogy is realized through a deformation groupoid interpolating between a reductive group and its motion group, and in this framework the Connes–Kasparov isomorphism appears as an operator-theoretic manifestation of the Mackey analogy, as developed notably in Higson’s work.
In this lecture, I will introduce the idea of Mackey correspondence and its relevance through the framework of reduced group C*-algebras.
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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