Day1
13:00
13:30-15.30
16:00 - 16:50
Ignasi Mundet
On a given symplectic manifold X, it is natural to expect that among all finite groups which admit continuous effective actions on X only a small subset may act in a symplectic and effective manner, and even fewer can inject in the group of Hamiltonian diffeomorphism groups. I will give several results confirming this expectation, and I will explain general
theorems and conjectures giving restrictions on which finite groups admit symplectic/Hamiltonian effective actions on a given symplectic manifold. Finally, I will motivate and give some evidence for a conjectural characterization of symplectic toric manifolds in terms of the finite abelian subgroups of the group of Hamiltonian diffeomorphisms. This will be a survey talk, and no prior knowledge on finite group actions or symplectic geometry will be assumed.
17:00 - 17:50
Marta Mazzocco
In this talk, I will explain how to apply the Fock-Goncharov construction to the representation theory of a class of algebras introduced by Etingof, Oblomkov and Rains which have deep and beautiful relations with b-symplectic structures on Del Pesso surfaces.
Slides:
18:00 - 18:50
Federica Pasquotto
Given an isolated hypersurface singularity, its link is a smooth manifold which carries a natural contact structure. In the 1960's, Mumford proved that any isolated singularity whose link is diffeomorphic to a sphere is actually a smooth point. In higher dimension, the diffeomorphism type of the link can fail to detect the singularity. Much more recently (2015), McLean showed that in dimension 5 additional information can be extracted from the contact structure of the link: more precisely, if the link of the singularity is contactomorphic to the standard sphere, then it is actually a smooth point.
This talk will be a gentle introduction to Milnor fibres, links and contact structures.
My interest in the topic is motivated by joint work with N. Adaloglou and A. Zanardini concerning symplectic invariants of contact structures on links of isolated hypersurface singularities.
Day2
12:00
Sala d'actes FME
Joaquim Brugués
15.00
16:00-18.30
Day 3
11:00
Sala d'Actes FME
Tom Mestdag
Nonholonomic constraints are velocity-dependent and non-integrable limitations on the possible motions of a mechanical system. In this talk, I will review some aspects of the almost symplectic and almost Poisson geometry behind Lagrangian systems with such constraints. In case of a kinetic-energy-Lagrangian, I will investigate the conditions under which the nonholonomic trajectories can be identified with geodesics of some Riemannian metric. This talk is based on joint work with M. Belrhazi.
12:00
Sala d'Actes FME
Sonja Hohloch
During the last decades, Floer homology turned out to be a powerful tool in many areas of mathematics with applications also to other sciences. In the original, classical setting, the generators of the chain groups of the homology are either transverse intersection points of two Lagrangian submanifolds or nondegenerate 1-periodic Hamiltonian orbits.
In this talk, we construct a Floer homology generated by transverse homoclinic points (= transverse intersection points of the stable and unstable manifold of a hyperbolic fixed point) of a symplectomorphism on a 2-dimensional symplectic manifold. This makes sense to be studied under the aspect of Floer homology since the stable and unstable manifolds of a symplectomorphism are Lagrangian submanifolds. The main challenge is the abundance of transverse intersection points generated by the chaotic intersection behaviour and how to define finitely generated chain groups with welldefined boundary operators.
13.30
16:00
Urs Frauenfelder
This is joint work with Agustin Moreno. Doubly symmetric periodic orbits play an important role in many problems in celestial mechanics as well as in the dynamics of atoms. For example, the direct and retrograde periodic orbit in Hill's lunar problem are doubly symmetric or Langmuir's periodic orbit in the dynamics of the Helium atom is doubly symmetric. In the talk, we show that a doubly symmetric
periodic orbit is never negative hyperbolic so that all its iterates are good orbits in the sense of Symplectic Field Theory (SFT). The proof of this result uses a real version of Krein theory and the GIT quotient.
17:00
Cédric Oms
Does a non-vanishing vector field always have a periodic orbit? This question was, and still is, a leading question that led to many beautiful results in the interplay between geometry, topology, and dynamical systems. In this talk, we will go through the history of this question, from the foundational works of Poincaré, to the developments led by Kupperberg, all the way to the contemporary developments in contact geometry. Time permitting, I will end the talk with recent advancements for $b$-contact geometry obtained in collaboration with Josep Fontana, Eva Miranda and Daniel Peralta-Salas.
This presentation is aimed at undergraduate students.