We will review recent developments in the area of algebraic K-theory and trace methods. The idea is to understand algebraic K-theory by comparing it to topological cyclic homology. In particular we shall explain how topological cyclic homology is related to arithmetic cohomology theories (like crystalline and prismatic cohomology) and how these relations lead to new insights.

Recording:
https://huji.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=a2971bb8-3c69-49a6-a68e-acef00e46507