Akira Tominaga: A duality in equivariant topological modular forms

Abstract: Hopkins-Mahowald introduced the spectrum (cohomology theory) TMF as a prominent example of spectra with chromatic height 2. The theme of this talk is the equivariant refinement of TMF, as constructed by Lurie and Gepner-Meier. I will discuss some computational results in U(1), U(n), and SU(n)-equivariant TMF, a strange duality phenomenon between U(n)-equivariant and SU(n)-equivariant cases, and its relation in algebraic geometry and representation theory of loop groups.