EVENT DETAILS AND ABSTRACT

Title: The algebraic K-theory of type 2 spectra
Speaker: Ishan Levy
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

The algebraic K-theory of the category of finite type n spectra is a fundamental object containing structural information about the stable homotopy category. However until recently almost nothing was known about it for n>1, primarily because it is not the K-theory of a connective ring. In this talk I will explain how, for n=2, it can be computed in terms of K-theory of discrete rings and topological cyclic homology. In particular, we can read off the K-groups in low degrees and find that there is an infinite family of 2-torsion classes in K_0 at the prime 2. I will also explain how to construct type 2 spectra representing these K_0 classes.