In this talk I will introduce the idea of Floer homotopy theory
and show how it can be used to give lower bounds on degenerate
Lagrangian intersections, in the case of plumbings of cotangent
bundles along a submanifold. The strength of the invariant...
In this talk, we begin by recalling Arnold’s geometric
formulation of hydrodynamics and then extend this framework to a
broader class of Hamiltonian systems, incorporating various PDEs
arising in mathematical physics. This motivates the study of...
We consider the symplectic area functional, constrained to loops
of vanishing Hamiltonian mean value: It has the same critical
points as the Rabinowitz action functional, and can be used to
define a similar Floer homology. In contrast to RFH, it...
This talk, which is based on two joint works, one with Pedro
Salomão and Richard Siefring and another with Michael Hutchings and
Vinicius Ramos, revolves around the role that restrictions on the
knot types of periodic Reeb orbits imposed by the...
The group of Hamiltonian diffeomorphisms , equipped with the
Hofer metric , is a central object in symplectic topology. A
landmark result by Polterovich and Shelukhin established the
profound geometric complexity of this group for surfaces and
their...
Locally conformally symplectic (LCS) manifolds are
generalisations of symplectic manifolds where the 2-form is not
closed but instead satisfies the identity dω = η ∧ ω for a closed
1-form η. The study of these manifolds is equivalent to that
of...
Given a symplectic 4-manifold it may admit multiple toric
fibrations. These can be seen as boundary points of the moduli
space of almost toric fibrations. We will sketch that all toric
fibrations are in the same connected component of this
moduli...
I'll introduce the genus zero open Gromov-Witten invariants for
even-dimensional Lagrangians. The definition relies on a canonical
family of bounding cochains satisfying the point-like condition of
Solomon-Tukachinsky, with non-commutative...
Helicity is an invariant of divergence free vector fields on a
three-manifold. One of its fundamental properties is invariance
under volume preserving diffeomorphisms. Arnold, having derived an
ergodic interpretation of helicity as an asymptotic...
I will begin by motivating the study of invariant distances on
spaces of Legendrians. I will then discuss two main results:
(a) the construction of a new unbounded invariant distance on the
universal cover of many Legendrian isotopy classes ;
(b) the...
