# 2016-2017 Geometric Structures Laboratory

July 1, 2016 to June 30, 2017, The Fields Institute

## Overview

The Geometric Structures Lab is hosted by the Fields Institute and engages in basic research at the interface of mathematics and physics.

Main focus areas include generalized geometry, Poisson geometry, the Hitchin system, the theory of Lie groupoids, the exact WKB method, the Riemann-Hilbert correspondence and the study of quantum field theory.

The Geometric Structures Lab typically meets on Tuesday and Thursday during the academic term from 11am - 1pm, unless otherwise indicated in the schedule, in the Stewart Library at The Fields Institute.

## Schedule

11:10 to 12:00 |
Vortex sheets and diffeomorphism groupoids
Anton Izosimov, University of Toronto |

10:00 to 11:30 |
Some applications of the BV-BFV formalism for field theories on manifolds with boundary
Alberto Cattaneo, Universität Zürich |

11:00 to 12:30 |
Uniqueness of Abelianization and Cluster Structures on Grassmannians
Omar Kidwai, University of Oxford |

10:00 to 12:00 |
Shifted Poisson structures: definitions, coisotropic structures, relation to shifted symplectic structures, (quasi-)Lie bialgebras, symplectic realizations
Pavel Safronov, University of Geneva |

10:00 to 12:00 |
Examples: (quasi-)symplectic groupoids, (quasi-)symplectic Lie algebroids, Courant algebroids, examples coming from groups
Pavel Safronov, University of Geneva |

10:00 to 12:00 |
Shifted symplectic structures: stacks, cotangent complex, differential forms, shifted symplectic/Lagrangian structures, Lagrangian intersections, mapping spaces
Pavel Safronov, University of Geneva |

11:10 to 13:00 |
Higher category for L_infty groupoids / String principal bundles and Courant algebroids
Chenchang Zhu, University of Goettingen |

11:10 to 13:00 |
Mirror symmetry for P^2 continued
Joey van der Leer Durán, University of Toronto |

11:10 to 12:00 |
Tensor structures, fiber functors, and Poisson structures defined by quasitriangular r-matrices
Victor Mouquin, University of Toronto |

11:10 to 13:00 |
Homological mirror symmetry for punctured Riemann surfaces from pair-of-pants decompositions
Heather Lee, Institute for Advanced Study |

11:10 to 12:00 |
Stokes phenomenon, Gelfand-Zeitlin systems and quantum groups
Xiaomeng Xu (MIT) |

11:10 to 13:00 |
No Title Specified
Francis Bischoff, University of Toronto |

11:10 to 13:00 |
The Landau-Ginzburg model mirror to P^2
Joey van der Leer Durán, University of Toronto |

11:10 to 12:00 |
On simplification near a simple turning point
Shinji Sasaki, University of Toronto |

11:10 to 13:00 |
Derived categories of del Pezzo surface (continued)
Mykola Matviichuk, University of Toronto |

11:10 to 12:00 |
Meromorphic line bundles (continued)
Kevin Luk, University of Toronto |

11:10 to 13:00 |
Derived categories of del Pezzo surface
Mykola Matviichuk, University of Toronto |

11:10 to 13:00 |
Meromorphic line bundles
Kevin Luk, University of Toronto |

11:10 to 13:00 |
Mirror Symmetry on an Elliptic Curve
Joshua Lackman, University of Toronto |

11:10 to 13:00 |
Algebroids from families of algebras
Michael Bailey, Utrecht University |

11:10 to 13:00 |
The Directed Fukaya Category of an Exact Morse Fibration
Paul Sacawa, University of Toronto |

10:30 to 12:00 |
A gentle introduction to gauge theory
Geoffrey Scott, University of Toronto |

11:10 to 13:00 |
The Maslov index and gradings in Floer cohomology
Charlotte Kirchhoff-Lukat, University of Cambridge |

11:10 to 13:00 |
Advanced integration by parts: the BV formalism
Theo Johnson-Freyd, Perimeter Institute |

11:10 to 13:00 |
Bounding chains and genus zero open Gromov-Witten theory
Sara Tukachinsky, Université de Montréal |

10:30 to 12:00 |
On fixed singularities in the exact WKB theory
Shinji Sasaki, University of Toronto |

11:10 to 13:00 |
Fukaya categories associated to Lefschetz fibrations
Francis Bischoff, University of Toronto |

10:30 to 12:00 |
Scalar curvature in Generalized Kaehler Geometry
Paul Sacawa, University of Toronto |

11:10 to 13:00 |
Fukaya categories associated to Lefschetz fibrations, talk 1
Joey van der Leer Durán, University of Toronto |

11:10 to 13:00 |
Morita bimodule approach to Generalized Kahler geometry
Francis Bischoff, University of Toronto |

11:10 to 13:00 |
A Construction of a Lax Equation
Joshua Lackman, University of Toronto |

11:10 to 13:00 |
Blow-ups in generalized complex and generalized Kähler geometry
Joey van der Leer Durán, University of Toronto |

11:10 to 12:00 |
Branes in stable generalised complex manifolds
Charlotte Kirchhoff-Lukat, University of Cambridge |

11:10 to 13:00 |
Quadratic differentials as stability conditions
Tom Sutherland |

11:10 to 13:00 |
Heterotic Courant algebroids by reduction
Lennart Döppenschmitt, University of Toronto |

11:10 to 12:00 |
Character varieties, quantum groups, and principal series representations
Alexander Shapiro, University of Toronto |

11:10 to 13:00 |
Singular points of planar foliations, part 2
Alberto Garcia-Raboso, University of Toronto |

11:10 to 13:00 |
The Exact WKB Method is Abelianisation
Nikita Nikolaev, University of Toronto |

11:10 to 13:00 |
Spaces of local systems from an abelianized point of view
Aaron Fenyes, University of Toronto |

15:30 to 16:30 | Riemann-Hilbert problems from Donaldson-Thomas theory |

11:10 to 13:00 |
Singular points of planar foliations, part 2
Alberto Garcia-Raboso, University of Toronto |

11:10 to 13:00 |
Derived intersections and applications
Márton Hablicsek, University of Pennsylvania |

11:10 to 13:00 |
Gromov width of Hamiltonian spaces
Jeremy Lane, University of Toronto |

11:10 to 13:00 |
Generalized Kahler geometry, part 2
Marco Gualtieri, University of Toronto |

11:10 to 13:00 |
Abelianization in action
Aaron Fenyes, University of Toronto |

11:10 to 13:00 |
Generalized Kahler geometry
Marco Gualtieri, University of Toronto |

11:10 to 12:00 |
Quantization, index theory, and Hamiltonian loop-group spaces
Yiannis Loizides, University of Toronto |

11:10 to 13:00 |
Geometric quantization and real polarizations
Marco Gualtieri, University of Toronto |

11:10 to 13:00 |
Bohr-Sommerfeld orbits and geometric quantization of the moduli space with a real polarization
Lisa Jeffrey, University of Toronto |

11:10 to 13:00 |
An overview of the exact WKB analysis of higher order equations (continued)
Shinji Sasaki, University of Toronto |

11:10 to 13:00 |
An overview of the exact WKB analysis of higher order equations
Shinji Sasaki, University of Toronto |

11:10 to 13:00 |
Riemann-Hillbert correspondence for flat connections with logarithmic singularities
Francis Bischoff, University of Toronto |

11:10 to 13:00 |
Singular points of planar foliations
Alberto Garcia-Raboso, University of Toronto |

11:10 to 13:00 |
Einstein field equations, Courant algebroids and Homotopy algebras
Anton Zeitlin, Columbia University |

11:10 to 13:00 |
Generalized Kähler vs Symplectic potential
Ahmed Zerouali, University of Toronto |

11:10 to 13:00 |
The Fock-Rosly Poisson structure and quasitriangular r-matrices
Victor Mouquin, University of Toronto |

11:10 to 13:00 |
Kirwan surjectivity in real symplectic geometry and moduli spaces of vector bundles over a real curve
Thomas Baird, Memorial University |

11:10 to 13:00 |
Quantized higher derived bracket construction for Courant algebroids
Mykola Matviichuk, University of Toronto |

11:10 to 13:00 |
Hitchin systems in geometry and physics
Aaron Fenyes, University of Toronto |

11:10 to 13:00 |
Baby steps toward geometric quantization
Aaron Fenyes, University of Toronto |

11:10 to 13:00 |
Deformation theory of Dirac structures via L∞ algebras
Mykola Matviichuk, University of Toronto |