Mathematics Department Colloquium: p-adic algebraic K-theory and topological cyclic homology

Colloquium | February 22 | 4-5 p.m. | 60 Evans Hall

 Akhil Mathew, University of Chicago

 Department of Mathematics

Algebraic K-theory is a basic invariant of rings connected to deep phenomena in arithmetic, geometry, and topology. When one works with the p-adic K-theory of p-adic rings, the theory of trace maps and the apparatus of topological cyclic homology (TC) is often a highly effective approximation used in many computations. The theory TC, while more conceptually involved than K-theory, is often easier to work with. In this talk, I will give a gentle introduction to these theories and explain their applications to some new structural results in K-theory.