Speaker
Daniel Álvarez , University of Toronto
Abstract
In this work we solve the problem of providing a Morita
invariant definition of Lie and Courant algebroids over Lie groupoids.
By relying on supergeometry, we view these structures as instances of
vector fields on graded groupoids which are homological up to homotopy.
We describe such vector fields in general from two complementary
viewpoints: firstly, as Maurer-Cartan elements in a differential graded
Lie algebra of multivector fields and, secondly, we also view them from
a categorical approach, in terms of functors and natural transformations.
Thereby, we obtain a unifying conceptual framework for studying many
examples. This is joint work with M. Cueca