Title: The Stringor 2-Bundle
Abstract: The Atiyah-Singer index theorem famously connects the index of Dirac operators on spinor bundles to push-forwards in K-theory. Ever since Witten's celebrated paper "The index of the Dirac operator on loop space" in 1987, much work in geometry and topology has been focused on constructing a "higher" version of this story. While the higher replacement for K-theory was constructed in the1994 by Hopkins, Mahowald, and Miller, the construction of a higher Dirac operator has remained elusive. In this talk I will discuss the notion of a "2-vector bundle", and the first construction of the stringor 2-vector bundle by Kristel, Luedwig, and Waldorf in 2022. If there is time, I will also discuss some recent work by myself and collaborators towards producing Dirac operators on stringor 2-bundles.
