Topological Censorship
Montag, 4.12.23, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
Prescription of Dirac Eigenvalues, Partial Eigenbundles and Surgery
Montag, 11.12.23, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
The prescription of eigenvalues of the Dirac operator on a closed spin manifold requires, besides the usual analytical methods à la Uhlenbeck and Dahl, also surgery methods to transport spectral data along a bordism. In this talk, I will give the necessary basics as well as an overview of the prescription of double eigenvalues on spin manifolds.
String Topology of Compact Symmetric Spaces
Montag, 18.12.23, 16:15-17:15, Raum 404, Ernst-Zermelo-Str. 1
On the homology of the free loop space of a closed manifold M there exists the so-called Chas-Sullivan product. It is a product defined via the concatenation of loops and can, for example, be used to study closed geodesics of Riemannian or Finsler metrics on M. In this talk I will outline how one can use the geometry of symmetric spaces to partially compute the Chas-Sullivan product. In particular, we will see that the powers of certain non-nilpotent homology classes correspond to the iteration of closed geodesics in a symmetric metric. Some triviality results on the Goresky-Hingston cohomology product will also be mentioned. This talk is based on joint work with Maximilian Stegemeyer.