will take place at the Amphithéâtre Descartes
of the École normale supérieure de Lyon, see the practical
information page for directions.
- Friday, January
- Alberto Abbondandolo,
On the length of the
geodesic on a Riemannian two-sphere
In 1988 Croke studied geodesic flows on a Riemannian two-sphere and
proved a uniform upper bound bound for the ratio between the square of
the length of the shortest closed geodesic and the area of the
two-sphere. The question of determining the best upper bound is still
open, but it is known that the round metric is not a global maximiser.
Babenko and Balacheff have conjectured that the round metric is a local
maximiser for the above ratio. In this talk I will discuss the proof of
a theorem which confirms this conjecture and complements it with a statement about the length of the longest simple closed
geodesic. This theorem was proved in collaboration with B. Bramham, U.
Hryniewicz and P. Salomão.
- Denis Auroux, Two
new constructions of monotone Lagrangian tori
We will discuss some recent constructions of "exotic" Lagrangian tori
in simple symplectic manifolds such as CP2
(work of Renato Vianna) and R6
that are not Hamiltonian isotopic to previously known examples,
inspired by wall-crossing phenomena and mirror symmetry.
- Roger Casals, Geometric
criteria for overtwistedness
In this talk, we focus on characterizing overtwisted contact
structures. First we introduce the overtwisted--tight dichotomy
in contact topology and detail the definition of the overtwisted disk.
Then we explain a criterion to detect whether a contact manifold is
overtwisted. In particular, we relate different notions of flexibility
and provide explicit examples of overtwisted contact manifolds. This is
joint work with E. Murphy and F. Presas.
- Georgios Dimitroglou
Rizell, Lagrangian unknottedness in
bundle of a torus and applications
The homotopically non-trivial Lagrangian tori in the cotangent bundle
of a two-torus are classified up to Hamiltonian isotopy. This is done
by following ideas and techniques due to Ivrii, who treated the case
when the torus is homologous to the zero-section. We apply this result
to obtain answers concerning the classification of monotone Lagrangian
tori in a symplectic vector space. Both questions are studied by
considering the behaviour of pseudo-holomorphic foliations when
stretching the neck around the Lagrangian submanifold.
- Urs Fuchs, Gromov
I will outline a proof of Gromov compactness for closed
pseudoholomorphic curves by following Gromov's original article and
emphasizing the study of the metrics induced on pseudoholomorphic
curves. Then I will indicate, how doubling constructions allow to carry
over this proof to situations, where the
pseudoholomorphic curves have totally real or otherwise controlled
boundary. This talk relies on joint work with Lizhen Qin.
- Stéphane Guillermou, Sheaves associated with exact Lagrangians
in cotangent bundles
The microlocal theory of sheaves associates with a sheaf its
microsupport which is a conic coisotropic subset of the cotangent
bundle. We will see how we can use this theory to recover recent
results on exact Lagrangians in cotangent bundles, namely that they
have Maslov class zero and that they are homotopy equivalent to the
- Ailsa Keating, Symplectic
properties of non-ADE Milnor fibres
Given any hypersurface singularity, Picard-Lefschetz theory readily
provides distinguished exact Lagrangian spheres (vanishing cycles) and
symplectomorphisms (Dehn twists about them). In the ADE (i.e., modality
zero) case, all exact Lagrangians are known to be spheres, and Dehn
twists generate the symplectic mapping class group in the A case. We will explain how
to construct exact Lagrangian S1xSn-1's in the
Milnor fibres of all non-ADE (i.e., positive modality) singularities.
The focus will be on modality one singularities in three variables.
Time allowing, we give applications to their symplectic mapping class
- Thomas Kragh, Simple
homotopy type of exact Lagrangians in cotangent bundles
I will start by recalling how the simple homotopy type of manifolds can
distinguish some smooth structures on manifolds with the same homotopy
type. I will then describe some recent progress, joint with M.
Abouzaid, where we prove that exact Lagrangians in cotangent bundles
are simple homotopy equivalent to the zero section, which thus provides
new restrictions on the smooth structure of exact Lagrangians.
- Vinicius Gripp Ramos, Billiards, toric domains and ECH capacities
ECH capacities have been shown to give sharp obstructions to many
symplectic embedding problems. In this talk, I will explain how they
are defined and give some examples of the problems for which they are
sharp. In particular, I will explain how to compute them for concave
toric domains and what that tells us about the space of billiard
trajectories on a round disk.
- Sobhan Seyfaddini, Unlinked fixed points of Hamiltonian
diffeomorphisms and a dynamical construction of spectral invariants
We construct a dynamical invariant, denoted by N, for Hamiltonians of
R2 and closed surfaces with positive genus. We prove that, on
the set of autonomous Hamiltonians, this invariant coincides with
the spectral invariants constructed by Viterbo on R and Schwarz on
closed surfaces of positive genus. This is joint work with
Vincent Humilière and Frédéric Le Roux.
- Anne Vaugon, Periodic
Reeb orbits and bypass attachments
Starting from a contact 3-manifold with boundary, a way to change the
contact structure is to choose a suitable Legendrian arc on the
boundary and glue to it half of a thickened overtwisted disk. This
elementary operation, called a bypass attachment, may yield a Reeb
vector field with additional periodic orbits. In this talk, I will
describe the new orbits created by a bypass attachment (for a
suitable choice of contact form) in terms of words on the Reeb chords
of the attaching arc. Following Giroux and Ozbagci, I will also explain
how a bypass attachment can be expressed as the combination on two
consecutive contact handle attachments, a point of view that may lead
to generalizations of the previous result.
- Naïm Zénaïdi, Lagrangian
Floer Theory for translated points of contactomorphisms
I will describe a Bott Framework of Lagrangian Floer theory
suitable to study pairs of cleanly intersecting Lagrangian submanifolds
with one positive end and explain how to use this set-up to obtain new
insights on the contact version of Arnold conjecture formulated in 2012
by S. Sandon.