## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**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.

**Date:** Monday, October 10, 2022

**Time:** 4:00pm

**Where:** Lunt 104

**Contact Person:** Benjamin Antieau

**Contact email:** antieau@northwestern.edu

**Contact Phone:** 847-491-5544

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