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Jonas Lente: Lectures

September 12, 2023
TITLE: Modular Mathai-Quillen currents

ABSTRACT: The Mathai-Quillen current is a correction term that appears in the Poincaré-Hopf theorem for manifolds with boundary, similar to the eta invariant in the Atiyah-Patodi-Singer theorem.
In this talk, I will explain how to extract a modular Mathai-Quillen current from modular cobordism invariants, such as the Witten genus. On the way, I will present an analogue of the Poincaré-Hopf theorem for supermanifolds. The hope is that this modular current provides a modular extension of the nu invariant for G_2-manifolds. This is part of my ongoing PhD project supervised by S. Goette and K. Wendland.