# Seminars & Events for Joint PU/IAS Symplectic Geometry Seminar

##### TBA

##### Dimers and Integrability

This is joint work with A. B. Goncharov. To any convex integer polygon we associate a Poisson variety, which is essentially the moduli space of connections on line bundles on (certain) bipartite graphs on a torus. There is an underlying integrable Hamiltonian system whose Hamiltonians are weighted sums of dimer covers.

##### Manifolds with G2 Holonomy and Contact Structures

A 7-dimensional Riemannian manifold (M,g) is called a G2 manifold if the holonomy group of its Levi-Civita connection of g lies inside G2. In this talk, I will first give brief introductions to G2 manifolds, and then discuss relations between G2 and contact structures. If time permits, I will also show that techniques from symplectic geometry can be adapted to the G2 setting. These are joint projects with Hyunjoo Cho, Firat Arikan and Albert Todd.

##### Construction of the Kuranishi structure on the moduli space of pseudo-holomorphic curves

To apply the technique of virtual fundamental cycle (chain) in the study of pseudo-holomorphic curve, we need to construct certain structure, which we call Kuranishi strucuture, on its moduli space. In this talk I want to review certain points of its construction.

##### Examples of nearly integrable systems with asymptotically dense projected orbits

**PLEASE NOTE SPECIAL TIME AND LOCATION.** The talk is intended to give examples of Arnold diffusion for nearly integrable systems which are very likely to be generic. We will describe an explicit perturbation of the flat metric on the three dimensional torus which admits orbits whose projection on their energy level become asymptotically dense in this level, when the size of the perturbation tends to 0. These examples can be seen as analogues of the initial Arnold model in which double resonances play the central role.