Real algebraic K-theory is a genuine $C_2$-spectrum which encodes three important invariants in topology: algebraic K-theory, Grothendieck-Witt theory, and L-theory. It is expected that real algebraic K-theory is well-approximated by real topological cyclic homology, a $C_2$-equivariant refinement of topological cyclic homology. In this talk, I will describe some techniques for computing real topological cyclic homology and give some sample applications. This is joint work with Jay Shah.

Speaker(s): J.D. Quigley (Cornell University)