# Algebra/Topology seminar

Craig Westerland (Minnesota), Cartier duality and topological T-duality

Abstract: Topological T-duality -- first investigated by Bouwknegt-Evslin-Mathai, Bunke-Schick, and others -- concerns a surprising duality isomorphism between twisted cohomology theories on different spaces.  It has traditionally been studied for twisted K-theory and deRham cohomology, owing to a physical origin where these objects can be considered as spaces of fields in a certain field theory.  In joint work with John Lind and Hisham Sati, we have established a general context in which duality theorems of this sort can be proven.  This context is naturally related to Cartier duality of finite Hopf algebras, and gives a host of new examples, particularly arising from chromatic homotopy theory.