Supersymmetric Field Theories and Derived Geometry

During my research leave, I will work on the following projects: 1) Batalin-Vilkovisky approach to field theory and superstring theory; 2) derived stacks, shifted symplectic structures, and applications in mathematical physics; 3) the topology of moduli spaces of real Riemann surfaces (i.e. Riemann surfaces with an orientation reversing involution). Project 1) is a joint project with Chris Hull, but parts of this project will also be carried out in collaboration with Alberto Cattaneo: the goal is to understand better the Batalin-Vilkovisky formalism in the presence of supersymmetry. (My recent work has shown that the analogies with ordinary symmetries are not as close as had been expected.) Project 2) is a continuation of my joint project with Kai Behrend: we are developing a general approach to the theory of higher stacks and derived higher stacks with a view to applications in analytic geometry. Project 3) develops from my work on the analogue of the Moore-Seiberg theorem in open-closed field theories: I hope to incorporate more general defects, such as cone points, into the geometric objects whose moduli are under consideration. My leave will be based at my home institution, but I will make extended trips of between 2 weeks and 2 months to the following institutions: Department of Physics at Imperial College, London, to work with Chris Hull; Department of Mathematics at University of British Columbia, to work with Kai Behrend; Department of Mathematics at University of Zurich, to work with Alberto Cattaneo; and Department of Mathematics at the Higher School of Economics, to work with Leonid Chekhov.