Events for 05/27/2020 from all calendars

Noncommutative Geometry Seminar

Time: 2:00PM - 3:00PM

Location: Zoom 942810031

Speaker: Zhizhang Xie, Texas A&M University

Title: Approximations of delocalized eta invariants by their finite analogues

Abstract: Delocalized eta invariants for self-adjoint first order elliptic differential operators on closed manifolds were first introduced by Lott, as a natural extension of the classical eta invariant of Atiyah-Patodi-Singer. It is a fundamental invariant in the studies of higher index theory on manifolds with boundary, positive scalar curvature metrics on spin manfolds and rigidity problems in topology. The delocalized eta invariant, despite being defined in terms of an explicit integral formula, is difficult to compute in general, due to its non-local nature. In this talk, I will report on some recent results concerning when the delocalized eta invariant associated to a regular covering space can be approximated by the delocalized eta invariants associated to finite-sheeted covering spaces, where the latter are easier to compute. This talk is based on joint work with Jinmin Wang and Guoliang Yu.

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