Appears in collection : 2023 IHES Summer School – Recent Advances in Algebraic K-theory

The scope of algebraic K-theory has been greatly extended by Alexander Efimov, who showed that it can be defined in a much broader categorical context than previously realized. This extended scope allows for precise connections with topology and analysis. I will give an introduction to Efimov's theory, and then focus on applications to complex geometry, the latter being joint work with Peter Scholze.