EVENT DETAILS AND ABSTRACT

Title: Quasi-elliptic cohomology
Speaker: Zhen Huan
Speaker Info: University of Illinois at Urbana--Champaign
Brief Description:
Special Note:
Abstract:

The elliptic cohomology associated to the Tate curve can be expressed as equivariant K-theory. I will introduce a theory Ell constructed by my advisor Charles Rezk. Its form is very similar to that of Tate K-theory but is not an elliptic cohomology, which brings its name "quasi-elliptic cohomology". Some constructions on the two theories have similar forms, such as the power operations, though some can be interpreted more easily on the new one. I will first set up the theory and show some properties of it. After that I will show my construction of its power operations following Nora Ganter's work, and then an application using its explicit form. I will also talk about the spectra representing it up to weak equivalence and show my construction of it. Moreover, the spectra can be "globalized" in Stefan Schwede's global homotopy theory.