Videos

Derived Algebraic Geometry And Its Applications - The Chern character and categorification

Presenter
March 29, 2019
Keywords:
  • Chern character
  • categorification
MSC:
  • 19F05
  • 18D05
  • 19d55
Abstract
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.