## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**Title:** Iterated K-theory of the integers and the Greek letter family red-shift conjecture

**Speaker:** Gabe Angelini-Knoll

**Speaker Info:** Michigan State University

**Brief Description:**

**Special Note**:

**Abstract:**

By work of Adams and Quillen, algebraic K-theory of the integers encodes special values of the Riemann zeta function. The denominators of these special values are also known to correspond to orders of the divided alpha family providing the beginning of a dictionary between homotopy and arithmetic. The Lichtenbaum-Quillen conjectures (LQC) suggest a more general relationship between algebraic K-theory groups and special values of Dedekind zeta functions. The red-shift conjectures of Ausoni-Rognes then generalize the LQC to higher chromatic heights in a precise sense. Inspired by these conjectures and the work of Adams and Quillen, I propose that the n-th Greek letter family is detected in the Hurewicz image of the n-th iteration of algebraic K-theory of the integers. In my talk, I will sketch a proof of this conjecture in the case n=2 using the theory of trace methods. Specifically, I show that the beta family is detected in the Hurewicz image of iterated algebraic K-theory of the integers. Consequently, by work of Behrens and Laures, iterated algebraic K-theory detects information about certain modular forms.

**Date:** Monday, March 04, 2019

**Time:** 4:10pm

**Where:** Lunt 104

**Contact Person:** Eva Belmont

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

**Contact Phone:** 847-467-1634

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