Title: A brief introduction to continuous K-theory
Abstract: Algebraic K-theory is an important object of large parts of algebra, geometry, and topology because of its universal role. However, a phenomenon often called the Eilenberg swindle has been accepted as a fundamental limit to the theory. Recently, Alexander Efimov introduced a construction called continuous K-theory which allows one to make sense of algebraic K-theory of certain large categories known as dualisable categories in a nontrivial way, solving the problem of Eilenberg swindle. In this talk, I will introduce dualizable categories and their localizing invariants. If time permits, I will explain some non-trivial results.