The Chern character and categorification
Derived algebraic geometry and its applications March 25, 2019 - March 29, 2019
Location: MSRI: Simons Auditorium
14F05 - Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
18D05 - Double categories, $2$-categories, bicategories and generalizations
19D55 - $K$-theory and homology; cyclic homology and cohomology [See also 18G60]
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.
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