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Graduate Student Homotopy Theory Seminar: Connor Grady, "The Stringor 2-Bundle"

Event Type
Department of Mathematics
207 Gregory Hall
Dec 1, 2023   3:00 pm  
Connor Grady
Samuel Hsu
Originating Calendar
Graduate Student Seminars in Mathematics
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.

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