5 jun 2015 -- 16:15
R. 423 (Konferenzraum)
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.