In the past decades, one of the most fruitful approaches to the study of algebraic K-theory has been trace methods, which constructs and studies trace maps from algebraic K-theory to topological Hochschild homology (THH) and related invariants. In recent years, theories of equivariant algebraic K-theory have emerged, but thus far few tools are available for the study and computation of these theories. In this talk I will introduce a trace methods approach to equivariant algebraic K-theory, discussing recent work constructing an equivariant Dennis trace map from equivariant algebraic K-theory to an equivariant version of THH. This is joint work with David Chan and Inbar Klang.
