# Trace methods for real algebraic K-theory

# Trace methods for real algebraic K-theory

**Zoom link: https://princeton.zoom.us/j/96282936122**

**Passcode: 998749**

Trace methods have long been used to study algebraic K-theory, but have been less successful in studying related invariants like Hermitian K-theory and L-theory. In this talk, I will give a progress report on the development of trace methods for these other theories. The key to this approach is real algebraic K-theory, which combines algebraic K-theory, Hermitian K-theory, and L-theory into a single genuine $C_2$-spectrum. In previous work, we developed a theory of real cyclotomic spectra which provided new tools for computing real topological cyclic homology, an approximation to real algebraic K-theory. I will recall our previous work, discuss recent generalizations, and share some new computations.

This is joint work with Jay Shah.