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...
Persistence modules and barcodes are used in symplectic topology
to define new invariants of Hamiltonian diffeomorphisms, however
methods that explicitly calculate these barcodes are often unclear.
In this talk I will define one such invariant...
The ellipsoidal embedding function of a symplectic four manifold
M measures how much the symplectic form on M must be dilated in
order for it to admit an embedded ellipsoid of some eccentricity.
It generalizes the Gromov width and ball packing...
The spectral norm provides a lower bound to the Hofer norm. It
is thus natural to ask whether the diameter of the spectral norm is
finite or not. During this short talk, I will give a sketch of the
proof that, in the case of Liouville domains, the...
