*Invariants of rings via equivariant homotopy*

Algebraic K-theory is an invariant of rings which illustrates a fascinating interplay between algebra and topology. Defined using topological tools, this invariant has important applications to algebraic geometry, number theory, and geometric topology. One fruitful approach to computing algebraic K-theory uses equivariant homotopy theory, a branch of algebraic topology which studies topological objects with a group action. In this talk I will give an introduction to algebraic K-theory and its applications, and talk about modern methods to compute algebraic K-theory.