Seminars Sorted by Series

After reviewing spectral invariants, I will write down an estimate, which under certain assumptions, relates the spectral invariants of a Hamiltonian to the C^0-distance of its flow from the identity. I will also show that, unlike the Hofer norm...

Legendrian contact homology (LCH) is a powerful holomorphic curves invariant for Legendrian submanifolds in contact manifolds. It is defined via a differential graded algebra (DGA), but the computation of its homology is often too difficult...

Seifert fibered 4-manifolds are the 4-dimensional analog of Seifert 3-manifolds in that these are the 4-manifolds which admit a fixed-point free smooth circle action. In this talk I'll first review what is known and then present some recent results...

Rabinowitzi-Floer homology is the semi-infinite dimensional Morse homology associated to an action functional which played a major role in the pioneering work of Rabinowitz. Critical points of Rabinowitz action functional are Reeb orbits while...

We will survey results (partly joint with Kleiner, and with Kleiner and Naor) on possibly fractal metric spaces which in a suitable sense have many rectifiable curves. We will try to cover: differentiable structure, a bi-Lipschitz nonembedding...

Floer homology generated by periodic orbits of Hamiltonian systems is, in general, not a classical homology theory. However, on phase spaces of cotangent bundle type for systems equivalent to the geodesic flow, all known structures in loop space...

Floer homology generated by periodic orbits of Hamiltonian systems is, in general, not a classical homology theory. However, on phase spaces of cotangent bundle type for systems equivalent to the geodesic flow, all known structures in loop space...

We will explain how to construct a symplectic Lefschetz fibration with explicit regular fiber and vanishing spheres which models a complexified Morse function on a cotangent bundle. We will sketch at the end how this leads to a definition of...

In this talk I shall sketch a proof of the following result: on a closed configuration space M, the Euler-Lagrange system associated to any time-periodic Tonelli Lagrangian function L : R/Z x TM --> R admits infinitely many periodic solutions. More...

Using a version of cylindrical contact homology on the complement of some Reeb orbits in a 3-dimensional contact manifold we will deduce that the existence of closed Reeb orbits with certain topological/dynamical properties implies the existence of...

There is a way to specify any smooth, closed oriented four-manifold using a surface decorated with simple closed curves, something I call a surface diagram. In this talk I will describe three moves on these objects, two of which are reminiscent of...

Predicting the future for a Hamiltonian dynamical system is an old and notoriously difficult problem. I will present some evidence however that in the simplest situation where one iterates an area preserving map on the 2-disk, solutions to an...

The restricted 3-body problem has an intriguing dynamics. A deep observation of Jacobi is that in rotating coordinates the problem admits an integral. In joint work with P. Albers, G. Paternain and O. van Koert, we proved that the corresponding...

The problem of capture in the planar restricted three-body problem is addressed. In particular, weak capture is described, which occurs at a complicated region called the weak stability boundary, where the motion is chaotic in nature. It was first...

In this talk we shall discuss the Cartan geometry of the rotating Kepler problem. The rotating Kepler problem appears as the limit of the restricted planar three-body body when one of the masses goes to zero. As such, this problem plays the role of...

Periodic bounce orbits are generalizations of billiard trajectories in the presence of a potential. Using an approximation technique by Benci-Giannoni we prove existence of periodic bounce orbits of prescribed energy. At the end of the talk I will...

We will discuss some recent SFT-type compactness results for J-curves (i.e. pseudo-holomorphic curves) in the symplectization of a contact manifold which is stretched along a special hypersurface. This procedure is called "sideways stretching" and...

The Dehn function is a group invariant which connects geometric and combinatorial group theory; it measures both the difficulty of the word problem and the area necessary to fill a closed curve in an associated space with a disc. The behavior of the...