## Project Details

### Description

I will work on the following projects: 1) Batalin-Vilkovisky approach to field theory and superstring theory; 2) higher stacks, derived stacks and shifted symplectic structures; 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 1 month 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.

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 1 month 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.

Status | Active |
---|---|

Effective start/end date | 9/1/17 → 8/31/22 |

### Funding

- Simons Foundation (524522)

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