06.11.2024, 14:00 - 16:00
– Campus Golm, Building 9, Room 2.22 and via Zoom
Institutskolloquium
Graphon Models for Inhomogeneous Random Graphs
Olga Klopp (Paris), Nicolas Verzelen (Montpellier)
Florian Hanisch
Integration over the space of superpaths, associated to a Riemannian manifold, plays an important role in the path integral approach to the Atiyah-Singer index theorem. This is indeed equivalent to integration of differential forms on the ordinary loop space and we will discuss the definition and properties of a suitable notion of integral, merging the Bosonic Wiener integral and a Fermionic counterpart. In particular, it allows us to integrate Bismut-Chern characters whose integrals give rise to indices of Dirac operators. If time allows, we will moreover sketch how our integral gives rise to an element in a canonically defined Pfaffian line bundle, making use of a zeta-regularized Pfaffian.