Enumerative mirror symmetry is a correspondence between closed
Gromov-Witten invariants of a space X, and period integrals of a
family Y. One of the predictions of Homological Mirror Symmetry is
that the closed Gromov-Witten invariants can be...
Powerful homology invariants of knots in 3-manifolds have
emerged from both the gauge-theoretic and the symplectic kinds of
Floer theory: on the gauge-theoretic side is the instanton knot
homology of Kronheimer-Mrowka, and on the symplectic the...
We show that for any closed symplectic manifold, the number of
1-periodic orbits of any non-degenerate Hamiltonian is bounded from
below by a version of total Betti number over Z, which takes
account of torsions of all characteristics. The proof...
In this talk, I will first discuss some instances in which
orbifolds occur in geometry and dynamics, in particular, in the
context of billiards and systolic inequalities. Then I will present
topological conditions for an orbifold to be a manifold...
The Hofer’s metric dH is a remarkable bi-invariant metric on the
group of Hamiltonian diffeomorphisms of a symplectic manifold. In
my talk, I will explain a result, obtained jointly with Matthias
Meiwes, which says that the braid type of a set of...
In this talk, we start by reviewing recent results on the
dynamics of Reeb vector fields defined by contact forms on
three-dimensional manifolds, and then introduce Reeb fields defined
by stable Hamiltonian structures. These are more general and...
Weinstein domains and their symplectic invariants have been
extensively studied over the last 30 years. Little is known about
non-Weinstein Liouville domains, whose first instance is due to
McDuff. I will describe two key examples of such domains in...
I will motivate the study of coproducts and describe a new
coproduct structure on the symplectic cohomology of Liouville
manifolds. Time permitting, I will indicate how to compute it in an
example to show that it's not trivial. This is based on my...
I will discuss how the Deligne-Mumford compactification of
curves arises from the uncompactified moduli spaces of curves as a
result of some algebraic operations related to (pr)operadic
structures on the moduli spaces. I will describe how a...
We present recent developments in symplectic geometry and
explain how they motivated new results in the study of cluster
algebras. First, we introduce a geometric problem: the study of
Lagrangian surfaces in the standard symplectic 4-ball
bounding...
