Joint IAS-PU Symplectic Geometry Seminar

Volume in Seiberg-Witten theory and the existence of two Reeb orbits

Daniel Cristofaro-Gardiner
University of California, Berkeley; Member, School of Mathematics
November 1, 2013

I will discuss recent joint work with Vinicius Gripp and Michael Hutchings relating the volume of any contact three-manifold to the length of certain finite sets of Reeb orbits. I will also explain why this result implies that any closed contact three-manifold has at least two embedded Reeb orbits.

Construction of the Kuranishi Structure on the Moduli Space of Pseudo-Holomorphic Curves

Kenji Fukaya
Simons Center for Geometry and Physics
April 12, 2013

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.

Dimers and Integrability

Richard Kenyon
Brown University
March 29, 2013

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.

Resonance for Loop Homology on Spheres

Nancy Hingston
The College of New Jersey; Member, School of Mathemtics
March 15, 2013

Fix a metric (Riemannian or Finsler) on a compact manifold M. The critical points of the length function on the free loop space LM of M are the closed geodesics on M. Filtration by the length function gives a link between the geometry of closed geodesics, and the algebraic structure given by the Chas-Sullivan product on the homology of LM and the “dual” loop cohomology product.

"Intermediate Symplectic Capacities"

Alvaro Pelayo
Washington University; Member, School of Mathematics
March 1, 2013

In 1985 Misha Gromov proved his Nonsqueezing Theorem, and hence constructed the first symplectic 1-capacity. In 1989 Helmut Hofer asked whether symplectic d-capacities exist if 1 < d < n. I will discuss the answer to this question and its relevance in symplectic geometry. This is joint work with San Vu Ngoc.