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郭昊 博士:Higher invariants in the maximal setting and their applications

本站小编 Free考研考试/2021-12-26
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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
Speaker: 郭昊 博士，Texas A&M University
Inviter:
Title:
 Higher invariants in the maximal setting and their applications
Time & Venue:
 2021.05.20 09:00-11:00 腾讯会议：215 544 787
Abstract:
 This talk focuses on higher index invariants that take values in the K-theory of certain maximal completions of geometric operator algebras. One reason for considering such completions is that they have better functoriality properties than their more common "reduced" counterparts. I will first discuss my work with Guoliang Yu and Zhizhang Xie, in which we prove that such completions are well-defined even when the manifold is non-compact but satisfies reasonable geometric properties, as well as a functional calculus for elliptic operators in the maximal setting. This makes it possible to give a geometric proof of the fact that the maximal higher index is functorial with respect to maps between covering spaces, and furthermore extends naturally to a proof of functoriality for the higher rho invariant. This has applications to the computation of such invariants. I will then discuss my joint work with Peter Hochs and Mathai Varghese on the indices of Callias-type operators that are invariant under the action of a locally compact group. This work generalises the notion of the coarse index from the setting of discrete group actions to continuous group actions, and has an application to the geometric quantisation commutes with reduction problem.

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