Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
| | Speaker: | 郭 昊 博士，Texas A&M University
| | Inviter: | | Title:
| Higher index theory of elliptic operators | Time & Venue:
| 2021.05.14 09:00-10:00 南楼N204室 | Abstract:
| 腾讯会议：226 859 659
In this talk, I will give an overview of my work and how it fits into the broader paradigm of higher index theory. The concept of the higher index is a far-reaching extension of the classical notion of Fredholm index that makes sense even for elliptic operators on non-compact manifolds. By taking into account the action of a group on the manifold, the higher index provides a link with the C*-algebra of the group. This has allowed many established and conjectured links to be made between analysis, geometry, topology, and operator theory. My work thus far has centred around studying the higher index theory of new classes of elliptic operators. This has led to applications to metrics of positive scalar curvature, computation of higher invariants, and the quantisation commutes with reduction problem in mathematical physics.
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