Soutenances de thèses :

Le 16 décembre 2022 à 14h - Bat. 9 - salle 109

Présentée par Grataloup Albin - IMAG

Derived Symplectic Reduction and Equivariant Geometry

Motivated by the cohomological construction for the BV formalism from physics, this thesis is asking the question of how to perform the intersections and quotients appearing in the BV construction. This leads to the study of the symplectic reduction procedure ``up to homotopy''.
Derived geometry is a natural tool to address such questions. In my thesis, I study the derived symplectic reduction for actions of groupoids and their infinitesimal counterpart, action of Lie algebroids. This generalizes the classical notion of moment maps. I also show that we can obtain ``shifted'' moment maps and symplectic reductions from a ``derived intersection'' procedure, providing interesting new examples of derived symplectic reduction.