Miquel Cueca: Deformations of Lagrangian Q-submanifolds

Abstract

The AKSZ sigma models are topological field theories with target given by a symplectic Q-manifold. Moreover, the Lagrangian Q-submanifolds of the target provide nice boundary conditions for these theories. In this talk, I will attach to every Lagrangian Q-submanifold an L∞-algebra, which controls its deformation theory (this construction is based on a graded version of Weinstein’s Lagrangian tubular neighborhood) and explain its geometric meaning. Finally, I will provide some explicit examples. This talk is based on a joint work with Jonas Schnitzer.