15:00 Yaroslav Kurylev (UCL): Geometric Whitney problem.
Whitney problem concerns with finding a finitely smooth function in a domain of Euclidian space which approximates a given one defined in a compact inside this domain (treat the latter as measurements). In this talk we discuss the geometric version of this problem in terms of the Gromov-Hausdorff distance between metric spaaces. This is a joint result with Ch. Fefferman (USA), S. Ivanov (Russia), M. Lassas (Finland) and H. Narayanan (USA).
16:30 Christian Baer (Potsdam): An index theorem for Lorentzian manifolds with boundary.
We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemannian manifolds with boundary. If time permits, an application to quantum field theory (the computation of the chiral anomaly) will be sketched. This is the first index theorem for Dirac operators on *Lorentzian* manifolds and, from an analytic perspective, the methods to obtain it are quite different from the classical Riemannian case. This is joint work with Alexander Strohmaier.