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The Chern character and categorification

Derived algebraic geometry and its applications March 25, 2019 - March 29, 2019

March 29, 2019 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Sarah Scherotzke (Westfälische Wilhelms-Universität Münster)
Location: MSRI: Simons Auditorium
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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.

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