The theory of higher Reidemeister torsion yields characteristic
classes of (stable) fiber bundles of smooth manifolds. We use this
theory to define a new family of invariants for Legendrians in
1-jet spaces which we collectively call Legendrian...
A well-known result of Abouzaid says that the wrapped Fukaya
category of a cotangent bundle is generated by one cotangent fiber.
In the filtered case this is not true, but the filtered Fukaya
category comes with a notion of interleaving distance. We...
The topological entropy of geodesic flows has been extensively
studied since the foundational works of Dinaburg and Manning. It
measures the exponential complexity of the geodesic flow of a
Riemannian manifold, and there are several results...
I will discuss some recent work establishing the orderability of
contact manifolds which arise as a quotient of an aspherically
fillable manifold by a finite group action which extends
(non-freely) to the filling. This generalizes the well known...
Let C be a closed surface and Σ⊂T*C a real exact Lagrangian
surface associated to a spectral curve. In this talk we will first
try to explain the context of this work (e.g., Higgs bundles and
spectral curves). We then construct a homomorphism from...
In a previous work with Felix Schlenk, we showed that an
analogue of the phenomenon of Lagrangian barriers holds in the
contact framework in S3 : there exist (explicit) Legendrian
complexes of arcs in S3 that have short Reeb chords to many...
In this talk, I will discuss the barcode entropy—the exponential
growth rate of the number of not-too-short bars—of the persistence
module associated with the relative symplectic cohomology SHM(K) of
a Liouville domain K embedded in a symplectic...
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...
