Speaker: Matt Ando (UIUC)

Title: A quasicategorical approach to Thom spectra and twisted Umkehr maps

Abstract: Let R be an associative ring spectrum. I shall describe several constructions of the R-module Thom spectrum associated to a map f : X \rightarrow BGL_1 R. The space BGL_1 R classifies the twists of R-theory, and to a fibration of manifolds g : Y \rightarrow X I shall associate an Umkehr map g! from the (f g)-twisted R-theory of Y to the f-twisted R-theory of X. In the case of K-theory, this twisted Umkehr map appears in the study of D-brane charge. I shall review this story, and then discuss the analogous construction for TMF.