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Spectral invariants eta and rho of Dirac operators

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 

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