Department of

October 2019 November 2019December 2019Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr SaSuMo Tu We Th Fr Sa 1 2 3 4 5 1 2 1 2 3 4 5 6 7 6 7 8 9 10 11 12 3 4 5 6 7 8 989 10 11 12 13 14 13 14 15 16 17 18 19 10 11 12 13 14 15 16 15 16 17 18 19 20 21 20 21 22 23 24 25 26 17 18 19 20 21 22 23 22 23 24 25 26 27 28 27 28 29 30 31 24 25 26 27 28 29 30 29 30 31

Tuesday, November 5, 2019

**Abstract:** Elliptic cohomology is a type of generalised cohomology theory related to elliptic curves which was introduced in the late 1980s. An important motivation for its introduction, which came from physics, was to help understand index theory for families of differential operators over free loop spaces. Yet for a long time, the only known constructions of elliptic cohomology were purely algebraic, and the precise connection to free loop spaces remained obscure. In this talk, I will summarise two constructions of complex analytic, equivariant elliptic cohomology: one from the K-theory of free loop spaces, and one from the ordinary cohomology of double free loop spaces. If time permits, I will also describe the construction of a Chern character-type map from the former to the latter.