##### Department of Mathematics,

University of California San Diego

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### Math 292: Topology seminar

## Ishan Levy

#### MIT

## The algebraic K-theory of type 2 spectra

##### 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.

Host: Zhouli Xu

### November 22, 2022

### 4:30 PM

APM 7218

Research Areas

Geometry and Topology****************************