Speaker: Andrew Macpherson
Title: Bivariant functors and bivariant theories
Abstract: Stable homotopy theory posits that cohomology theories can be
regarded as a "first order" approximation to homotopy types. If so,
then cohomology theories *with transfers* are a first order
approximation to *motivic* or *geometric* types.
This class of objects is most neatly defined in the setting of
(∞,2)-category theory, where they (or their categorified cousins) are
corepresented by a (∞,2)-category of spans. In this talk I will
describe a "syntactic" approach to these constructions and the proof of
the universal property that avoids the use of explicit simplicial
constructions and echoes methods from classical localisation theory.