“K-theory: from analysis to homotopy theory”
Matedì 29 Aprile 2025, ore 17:00 - Aula 2AB45 - Valerio Bianchi (PhD Student Cardiff University)
Abstract
Topological K-theory was developed by Atiyah and Hirzebruch in 1961 based on Grothendieck’s work on algebraic varieties. The idea is to capture the topology of a space X by studying vector bundles over it. It is possible to define K-theory directly from X, or in terms of matrices of continuous complex-valued functions on X. This provides a more algebraic approach which extends to matrices over general Banach algebras. In fact, since the early 1970s Ktheory has been a powerful tool in C∗-algebras theory. I will give an introduction to this topic and present some instances of the interplay between operator algebras and homotopy theory.
