Bertrand Toen
Title: Topological invariants for non-commutative schemes
Abstract: This talk is a report on a recent work of Anthony Blanc. I will start by recalling the setting of non-commutative geometry in the sense of Bondal, Kontsevich, Van den Bergh, based on associative dg-algebras. I will also recall the existence of moduli spaces (or rather stacks) of sheaves on non-commutative schemes. I will then explain how these moduli spaces can be used in order to define topological K-theory of non-commutative schemes, as well as to prove that the algebraic chern character with values in periodic cyclic homology factors throught topological K-theory. I will finish the talk with some open questions, relevant to non-commutative Hodge theory in the sense of Katzarkov-Kontsevich-Pantev, Kaledin.