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 Oancea****, ****University
of
Strasbourg
and
IAS
**

__Title__**:**

**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

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