Symplectic and Differential Geometry Seminar
Vanderbilt University

   Spring 2012

   Organizers:  Basak Gurel and Ioana Suvaina

   Tuesdays, 2:30-3:30pm in SC 1312 (unless otherwise noted)

   Related seminars also announced.

Tuesday, February 7th, 2012,

Speaker: Rares Rasdeaconu, Vanderbilt University

Title: The Asymptotic Behaviour of the Welschinger Invariants

Abstract The Welschinger invariants are integers providing lower bounds for the number of
real rational curves on real algebraic manifolds of small dimension. In this talk I will present
some of the results I obtained in a joint work with J.-Y. Welschinger regarding the asymptotic
behavior of the Welschinger invariants for small number of real constraints. Our method is
based on ideas from the symplectic field theory.


Tuesday, February 14th, 

Speaker: Strom Borman University of Chicago

Title: Computing filtered Hamiltonian Floer homology

Abstract: For many quantitative applications of Floer theories, one is required to compute the
homology with respect to some filtration and in practice this can be difficult.  In this talk I will
outline a strategy for turning certain filtered Hamiltonian Floer homology computations into
contact homology computations.  The proof of this strategy requires a general compactness theorem,
which includes `stretching the neck' for Hamiltonian Floer trajectories, and generalizations of
Bourgeois--Oancea's work relating symplectic homology with contact homology.  This is joint
work in progress with Y. Eliashberg and L. Polterovich, and is part of a larger project with L. Diogo
and S. Lisi.

Thursday, February 16th, Colloquium

Speaker: Alexandru OanceaUniversity of Strasbourg and IAS



Friday-Saturday, February 16th-17th, Shanks Workshop: Symplectic Topology and Hamiltonian Dynamics

Speakers: P. Albers, V. Ginzburg, M. McLean, A. Momin, A. Oancea, M. Usher


Tuesday, March 27th

Speaker: Garrett Alston, Kansas State University

Title: Involutions in Floer theory

Abstract: One way to try to understand a symplectic manifold is to try to understand its Lagrangian
submanifolds. Two general interesting types of Lagrangian submanifolds are Lagrangian torus fibers
and fixed point sets of antisymplectic involutions. A key invariant of the Lagrangians is their Floer
cohomology, which in general is difficult to compute. However, antisymplectic involutions provide
some general techniques that can be used to try to compute it. In this talk I will survey some of the
known results in this direction.

Tuesday, April 17th

Speaker: Olguta Buse, IUPUI

Title: Symplectic ellipsoid embeddings in higher dimensions and packing stability

                  Abstract: Motivated by a search for strong  reccurence properties of symplectic mappings Gromov
                asked for the maximal sizes of balls for which $k$ disjoint copies can be symplectically embedded
                simultaneously  into a given symplectic manifold. If the total volume of the the balls matches that of
                the target manifold, one says that they are volume filling.
                The symplectic packing stability conjecture, proved in the mid- nineties by Paul Biran for most four
                dimensional manifolds, states that for all numbers $k$ sufficiently large one can always get a volume
                filling symplectic $k$ -embedding into a given symplectic  manifold.
                We will present a proof for this conjecture for all symplectic manifolds with rational cohomology classes.
                The main  tool that we prove and use is the flexibility of symplectic ellipsoid embeddings in all dimensions.
                This is joint work with Richard Hind.

Old Seminar Web-Pages: Fall 2009, Fall 2010, Spring 2011, Fall 2011