# Seminars & Events for Symplectic Geometry Seminar

##### Coherent-constructible correspondence and its applications

I will describe a coherent-constructible correspondence, which is a monoidal dg functor between the category of equivariant perfect sheaves of a toric variety and the category of some constructible sheaves over a real vector space (dual Lie algebra of the torus). This correspondence is motivated by homological mirror symmetry - performing a T-duality on an equivariant line bundle produces a Lagrangian submanifold in the cotangent bundle of that dual Lie algebra. The Nadler-Zaslow's theorem then equates this Lagrangian to a constructible sheaf on the base. This correspondence can be extended to toric DM stacks, and as an exercise, one may show the derived categories are equivalent from the combinatorial constructible viewpoint in the case of some toric crepant resolutions.

##### Schrödinger equation, deformation theory and $tt^*$ geometry

I will talk about my recent work on the deformation theory of Schrödinger equations. This is an attempt to construct the rigorous mathematical foundation for topological B model, which has tight relation to the deformation theory of complex structure and the singularity theory.

##### Canonical Kahler metrics and the K-stability of projective varieties

The "standard conjectures" in Kahler geometry state that the existence of a canonical metric in a given Hodge class is equivalent to the stability of the associated projective model(s). There are several competing definitions of stability ( mainly due to Tian and Donaldson ) and various partial results linking these definitions to the sought after metric. I will give a survey/progress report of my own work on this problem. The reference for the talk is: http://arxiv.org/pdf/0811.2548v3

##### A conjecture of Arnold

The *chord conjecture* of Vladimir Arnold is a contact-geometry analogue of his well-known Lagrangian intersections conjecture in symplectic geometry. It proposes that, for each Legendrian submanifold of a contact form on a compact manifold, there should be a integral curve of the Reeb vector field which crosses the Legendrian submanifold at least twice. I will present the 2001 paper of Klaus Mohnke, which proves this conjecture for a class of compact contact manifolds including spheres.

##### Aspects of stringy global quotients, de Rham, singularities and gerbes

We discuss stringy functors from the pull back point of view of Jarvis-K-Kimura and the push forward point of view of our orbifold Milnor ring constructions. We show how these approaches merge to give a de Rham theory and apply back to singularity theory. If time allows, we also give results on global gerbe twists and the Drinfel'd Double.