May 6, 2025 3:30 pm
Transportation Building 203
- Sponsor
- Department of Mathematics
- Speaker
- Alex Taylor (Illinois)
- Contact
- Pierre Albin, Eric Chen, Pei-Ken Hung, Gabriele La Nave
- palbin@illinois.edu, ecchen@illinois.edu, pkhung@illinois.edu, lanave@illinois.edu
- Views
- 49
- Originating Calendar
- Mathematics Seminar Series: Geometric Analysis
Title: An index formula for families of end-periodic Dirac operators
Abstract: The famous Atiyah-Patodi-Singer (APS) index theorem gives a geometric formula for the Fredholm index of a Dirac operator on a compact manifold with boundary. In 2014 Mrowka-Ruberman-Saveliev extended the theorem to end-periodic (asymptotically periodic) manifolds. On the other hand, there is a stronger version of the APS index theorem for families of Dirac operators established by Bismut-Cheeger (1990) and then further developed by Melrose-Piazza (1997). I'll discuss this story and present a new index formula for families of end-periodic Dirac operators.