• 2:10-2:25  Yucong Jiang, University of Toronto

Generalized Kahler geometry and symplectic double groupoids

Generalized Kahler (GK) geometry is a type of geometry on the target space of a N=(2,2) supersymmetry nonlinear sigmal model discovered by Gates, Hull and Roc̆ek in 1984. Later on, It was formulated in terms of generalized complex structures by Gualtieri in his thesis in 2004. Under this framework, a GK structure can also be formulated in terms of a pair of holomorphic Manin triples. We will take this as the starting point and employ techniques from Poisson geometry to study GK structures. We found that there are holomorphic double symplectic Morita equivalences between symplectic double groupoids which also equipped with smooth Lagrangian branes encoded the information about the underlying generalized Kahler metric of the space. Our result extends a previous result of the symplectic type case and allows the background 3-form to be not exact. This is a joint work with Daniel Alvarez and Marco Gualtieri.

• 2:30-2:45  Jie Min, University of Massachusetts, Amherst

Moduli of symplectic log Calabi-Yau divisors and torus fibrations

Symplectic log Calabi-Yau divisors are the symplectic analogue of anti-canonical divisors in algebraic geometry. We study the rigidity of such divisors. In particular we prove a Torelli type theorem and form an equivalent moduli space of homology configurations which is more suitable for enumerative problems. We also discuss their relations to toric actions and almost toric fibrations.

• 2:50-3:05  Luka Zwaan, University of Illinois at Urbana-Champaign

Duistermaat-Heckman results for Hamiltonian groupoid actions

I will talk about work in progress where I attempt to generalize the classical Duistermaat-Heckman results to the setting of Hamiltonian actions of (regular, source proper) symplectic groupoids. In the case of a free action, we can apply the results of Crainic, Fernandes and Martinez-Torres on PMCTs to the quotient. When the action is locally free, the quotient will in general only be a Poisson orbifold. In this case, we will instead analyze the DMCT that presents it.

• 3:10-3:25  David Miyamoto, University of Toronto

The Basic Complex of a Singular Foliation

A singular foliation F gives a partition of a manifold M into leaves whose dimension may vary. Associated to a singular foliation are two complexes, that of the diffeological differential forms on the leaf space M/F, and that of the basic differential forms on M. We prove the pullback by the quotient map provides an isomorphism of these complexes in the following cases:
 - when F is a regular foliation,
 - when points in the leaves of the same dimension assemble into an embedded (more generally, diffeological) submanifold,
 - and, as a special case of the latter, when F is induced by a linearizable Lie groupoid.