# Prof. Dr. Christian Bär (Universität Potsdam) "From Gauss-Bonnet to particle-antiparticle creation"

Jun 05, 2015 from 04:15 PM to 05:15 PM

**Abstract:
**

The Gauss-Bonnet formula expresses the Euler number of a closed surface
in terms of its curvature. This formula is a classical special case of
the Atiyah-Singer index theorem, one of the main mathematical results of
the 20. century.
The index formula relates the index of certain partial differential
operators with the geometry of the underlying space. If one allows
nonempty boundary, this leads to the Atiyah-Patodi-Singer index formula.

After a survey over these classical results we will discuss recent
work with A. Strohmaier where spaces are replaced by spacetimes. The
resulting PDEs are hyperbolic rather than elliptic.
Even though the analysis is entirely different, an analog to the
Atiyah-Patodi-Singer index formula has been found. The boundary
conditions now have a natural physical interpretation.