Research Group:
Speaker:
Sara Azzali
Institution:
University of Potsdam
Schedule:
Friday, April 1, 2016 - 11:30
Abstract:
We give an introduction to spectral invariants "eta" and "rho" of Dirac operators, their role in index theory, and some of their applications to geometry.
The eta invariant of a Dirac operator was introduced in 1975 by Atiyah, Patodi and Singer in the series of seminal papers "Spectral asymmetry and Riemannian Geometry", motivated by the signature formula for a manifold with boundary.
Eta is a nonlocal object, but its variation is basically formed by local quantities. For this reason, the difference of two eta invariants (of locally equivalent operators) is a much more stable object (called a rho invariant) that can be used to distinguish geometric structures.
After an overview of the classical constructions and properties of rhotype invariants, we will present some of the recent developments and directions of research related to noncommutative geometry.
Venue: Department of Mathematics, Trieste University, Seminar Room - Third Floor bld H2bis