Some observations towards the algebraic index theorem

GAP Seminar

Meeting Details

For more information about this meeting, contact Nigel Higson, Mathieu Stiénon, Ping Xu.

Speaker: Ryan Grady, Notre Dame

Abstract: This talk is largely based on joint work with O. Gwilliam (Northwestern) where we build a quantum field theory which we call topological quantum mechanics. The construction is a dance through the realms of derived geometry, effective field theory, and the Batalin-Vilkovisky formalism. The global observables of topological quantum mechanics, which are a deformation of de Rham forms by the partition function, encode the Todd class (resp. the \hat{A} class in the smooth setting) of the manifold over which the theory lives. By performing a more refined analysis of the observables we recover differential operators and a new proof of the algebraic index theorem of Nest and Tsygan. No familiarity with quantum field theory will be assumed in this talk.

Room Reservation Information

Room Number: 106 McAllister

Date: 11/15/2011

Time: 2:30pm - 3:30pm