Workshop, Alejandro Cabrera: Symplectic supergeometry behind the Mathai-Quillen formalism and applications

Speaker
Alejandro Cabrera, UFRJ, Brazil

Abstract
In this talk, we shall give a general (odd and even) symplectic perspective on the Mathai-Quillen (MQ) formalism of characteristic classes of vector bundles. The key result is the geometric construction of a gauge-fixing Lagrangian submanifold leading to MQ-formulas. We then apply these results in the context of Topological Field Theories to obtain known and new localization results. This is joint work with F. Bonechi.