All talks will be held in S-240, in the basement of the Math Building. The registration desk will be open during the hours of the conference; coffee and other refreshments will be available as well. In addition, a light breakfast will be served on the three mornings of the conference. A wine-and-cheese welcome reception will follow the opening talk in S-240.

Talks & Abstracts

October 12, 2006
4:00 PM - 5:00 PM
Dietmar Salamon, ETH Zürich
Pseudoholomorphic Curves in Symplectic Topology

October 12, 2006
5:30 PM - 7:00 PM
Wine-and-Cheese Welcoming Party

October 13, 2006
09:15 AM - 12:45 PM
Presentations by Young Researchers,

Speakers: Joseph Johns (NYU), Dagan Karp (Berkeley), Davesh Maulik (Princeton), Brett Parker (MIT), Rosa Sena-Dias (MIT/IST). See the Mini-Workshop page for the list of titles and abstracts.

October 13, 2006
2:15 PM - 3:15 PM
Helmut Hofer, NYU
Generalized Fredholm Theory

October 13, 2006
3:45 PM - 4:45 PM
Susan Tolman, UIUC
A Very Generalized Schubert Calculus

Based on joint work with R. Goldin. Schubert calculus is the calculus of enumerative geometry. One of the main goals is to find nice combinatorial descriptions of the structure constants of the cohomology ring of the Grassmanian in terms of its natural geometric Shubert basis Our goal is to consider the same question in the much broader context of symplectic manifolds with Hamiltonian torus actions. We show that if there exists an invariant Palais-Smale metric, then the structure constants can be computed as a weighted sum over paths in a certain graph.

October 13, 2006
5:00 PM - 6:00 PM
Francois Lalonde, Montreal
Relative Capacities and a Real Quantum Product

We explore operations between the Lagrangian cluster complex and the ambiant quantum homology. We define a notion of relative capacity and a real quantum product that should relate to Ceyhan-Welschinger product. These ideas are related to Albers' work and Biran-Cornea's work in CPn. Joint with Octav Cornea.

October 13, 2006
7:00 PM - 10:00 PM
Port Jefferson
Banquet at Lombardi's

Please register by noon 10/13 if you have not already done so. Click here for details, directions, etc.

October 14, 2006
09:45 AM - 10:45 AM
Ragni Piene, Oslo
Enumerating Singular Curves on a Surface

Given a family of curves on an algebraic surface and a set of curve singularity types, there is a natural cycle representing curves of the family that have such singularities. The goal is to compute these cycle classes, or even to determine their generating functions. I shall report on joint work with S. Kleiman on this problem.

October 14, 2006
11:15 AM - 12:15 PM
Rahul Pandharipande, Princeton
Counting Disks

Recently, J. Solomon has defined an enumerative theory of holomorphic disks with boundary in a real Lagrangians. I will discuss a calculation of these disk invariants in the basic case of the Calabi-Yau quintic. The talk represents joint work with Solomon and J. Walcher.

October 14, 2006
2:00 PM - 3:00 PM
Ivan Smith, Cambridge
Exact Lagrangian Submanifolds Revisited

This talk reports on joint work-in-progress with Kenji Fukaya and Paul Seidel. We combine ideas from homological mirror symmetry with properties of Fukaya categories of affine varieties, to study exact Lagrangian submanifolds in cotangent bundles.

October 14, 2006
3:20 PM - 4:20 PM
Kenji Fukaya, Kyoto
Homological Algebras for Open Gromov-Witten Theory

October 14, 2006
4:30 PM - 5:30 PM
Yakov Eliashberg, Stanford
Contact Homology and Legendrian Surgery

I will discuss different flavors of contact homology and Legendrian contact homology, and relations between them.

October 15, 2006
09:00 AM - 10:00 AM
Victor Guillemin, MIT
Classical and Quantum Birkhoff Canonical Forms

I will discuss in this talk some inverse spectral results which say that the spectrum of a quantum mechanical system determines the behavior of the corresponding classical system in a "formal" neighborhood of a periodic trajectory. In particular I'll report on some recent work in this area involving the "bottom of the well" spectral asymptotics of the Schroedinger operator.

October 15, 2006
10:20 AM - 11:20 AM
Dennis Sullivan, Stony Brook
String Topology and Contact Homology

We will compare the algebraic forms of the operations of the string topology related to the top strata of Riemann' moduli spaces and the algebraic form of the operations in symplectic field theory (absolute and relative) related to rigid holomorphic curves (the bottom strata of Gromov's moduli spaces).

Department of Mathematics, Stony Brook