Loop space constructions of elliptic cohomology
I will summarise two constructions of Grojnowski's torus-equivariant elliptic cohomology. The first is obtained as the equivariant K-theory of the single free loop space LX, and is based on the work of Kitchloo. The second is obtained as the equivariant cohomology of the double free loop space LLX, and is based on the work of Rezk. I will present the two constructions in a way that emphasises the high degree of formal similarity between them, and if time permits, I will also mention the construction of a Chern character-type map from the former to the latter.
Dr Matthew Spong, University of Melbourne