Top-level heading

The categorified Grothendieck-Riemann-Roch Theorem

Categoria: 
Seminari di Algebra e Geometria
Data e ora inizio evento: 
Data e ora fine evento: 
Aula: 
Sala di Consiglio
Sede: 

Dipartimento di Matematica, Sapienza Università di Roma

Speaker: 

Sarah Scherotzke (Université du Luxembourg)

The Chern character is a central construction which appears in topology, representation theory and algebraic geometry. In algebraic topology it is for instance used to probe algebraic K-theory which is notoriously hard to compute, in representation theory it takes the form of classical character theory. Recently, Toen and Vezzosi suggested a construction, using derived algebraic geometry, which allows to unify the various Chern characters. We will categorify this Chern character. In the categorified picture algebraic K-theory is replaced by the category of non-commutative motives. It turns out that the categorified Chern character has many interesting applications. For instance we show that the DeRham realisation functor is of non-commutative origin.