Modul: MAT070 Zurich Colloquium in Mathematics

## Algebraic K-Theory and higher algebra

Talk by Prof. Dr. Thomas Nikolaus

**Date:** 01.11.22 **Time:** 16.30 - 18.00 **Room:**

This talk is about algebraic K-theory groups (defined by Quillen in the early 1970s). We will review the definition and motivation behind those groups and explain some applications.

Then we try to summarise what is known in terms of computations and explain some recent breakthroughs (based on so-called trace methods). One of the central tools used to achieve this progress is`higher categorical algebra' in the sense of Waldhausen, Lurie and others. As an sample application we cover the recent results on the K-theory of Z/p^n obtained in joint work with Anteau and Krause.