To an element in the completion of the set of Lagrangians for
the spectral distance we associate a support. We show that
such a support is γ-coisotropic (a notion we shall define in the
talk) and we shall give examples and counterexamples of γ...
In this talk, I want to show that in the planar circular
restricted three body problem there are infinitely many symmetric
consecutive collision orbits for all energies below the first
critical energy value. By using the Levi-Civita
regularization...
Let K be a knot or link in the 3-sphere, thought of as the ideal
boundary of hyperbolic 4-space, H4. The main theme of my talk is
that it should be possible to count minimal surfaces in H4 which
fill K and obtain a link invariant. In other words...
The Hochschild cohomology of the Floer algebra of a Lagrangian
L, and the associated closed-open string map, play an important
role in the generation criterion for the Fukaya category and in
deformation theory approaches to mirror symmetry. I will...
The existence of rational plane curves of a given degree with
prescribed singularities is a subtle and active area in algebraic
geometry. This problem turns out to be closely related to difficult
enumerative problems which arise in symplectic field...
I will talk about an ongoing project that explores the
construction of high dimensional Legendrian spheres from supporting
open books and contact structures. The input is a Lagrangian disk
filling of a Legendrian knot in the binding. We try to...
I will explain the construction of a new class of Liouville
domains that live in a complex torus of arbitrary dimension, whose
boundary dynamics encodes information about the singularities of a
toric compactification. The primary motivation for this...
In this talk, we will study the Floer Homology barcodes from a
dynamical point of view. Our motivation comes from recent results
in symplectic topology using barcodes to obtain dynamical results.
We will give the ideas of new constructions of...
I will review two combinatorial constructions of integrable
systems: Goncharov-Kenyon construction based on counting perfect
matchings in bipartite graphs, and
Gekhtman-Shapiro-Tabachnikov-Vainshtein construction based on
counting paths in networks...
In a work with Jacques Fejoz, we consider the conformal dynamics
on a symplectic manifold , i.e. for which the symplectic form is
transformed colinearly to itself. In the non-symplectic case, we
study the problem of isotropy and uniqueness of...
