Speaker
Dr
Emanuele Pavia
(University of Luxembourg)
Description
One of the most celebrated and far-reaching achievements in algebraic geometry is the concept of (perfect) obstruction theory introduced by Behrend and Fantechi. Roughly, this amounts to replacing unbounded cotangent complexes of (very singular) stacks with smaller complexes in order to produce and compute numerical invariants.
In this talk, we describe how this machinery can be generalized to the supergeometric setting, thanks to the powerful formalism of homotopical algebra. As a possible application, we hint at the construction of an obstruction theory for the moduli superstack of stable supermaps.
This is based on joint work in progress with U. Bruzzo, D. Hernández Ruipérez, and A. Ricolfi.
