# Mini-Workshop on Symplectic Geometry

10/07/2015

VU Amsterdam

Mini-Workshop on Symplectic Geometry on 7 October 2015 at VU Amsterdam

Faculty of Science

Sciences

Conference / Symposium / Seminar

On October 7, 2015 the Vrije Universiteit Amsterdam will host a Mini-Workshop on Symplectic Geometry, click here for the poster.

The speakers will be Leonid Polterovich (Tel Aviv), Alexandru Oancea (Paris), Barney Bramham (Bochum), and Sheila Sandon (Strasbourg).

This mini-workshop is aimed at researchers, Ph.D. students, and advanced master's students working in symplectic geometry and related areas. It is supported by the clusters NDNS+ and GQT.

This is the second instance of what will hopefully become a biannual tradition. The goal of these mini-workshops is to strengthen the symplectic community of the Netherlands and to connect it with abroad.

For questions, please contact the organizers: Oliver Fabert (VU Amsterdam) and Fabian Ziltener (Utrecht).

**Registration: **

Please register - here is the current list of registered participants.

*Schedule:*

09:30-10:00 Welcome with coffee

10:00-11:00 Barney Bramham

11:00-11:30 Coffee break

11:30-12:30 Margherita Sandon

12:30-14:00 Lunch break

14:00-15:00 Alexandru Oancea

15:00-15:30 Coffee break

15:30-16:15 Leonid Polterovich - Colloquium talk

16:30-17:15 Leonid Polterovich

19:00 Dinner at De Veranda (directions from googlemaps)

**Directions:**

All lectures take place in room HG 10A20 on the 10th floor of the main building (hoofdgebouw). When you enter the VU at the main entrance (1105), walk left to the elevators, use them to get the 10th floor; room HG 10A20 is directly next to the elevators. Here is a map of the VU campus.

VU University Amsterdam is best reached via train station Amsterdam Zuid which served by all trains running between Schiphol and Utrecht. From Amsterdam Zuid station it is a 5-10 minutes walk to the VU - or you take the metro 51 to Westwijk and exit directly at the next stop De Boelelaan/VU/VU medisch centrum. Here you find further directions.

*Abstracts:*

*Leonid Polterovich - Colloquium talk:*

**Geometry of symplectic transformations: 25 years after**

In 1990 Helmut Hofer introduced a bi-invariant metric on symplectomorphism groups which nowadays plays an important role in symplectic topology and Hamiltonian dynamics. I will review some old, new and yet unproved results in this direction.

*Leonid Polterovich:*

**Hamiltonian diffeomorphisms and persistence modules**

I'll discuss robust obstructions to representing a Hamiltonian diffeomorphism as a full power, with applications to geometry and dynamics. The approach is based on the theory of persistence modules. Joint work with Egor Shelukhin.

*Alexandru Oancea:*

**Finiteness of the Hofer-Zehnder capacity in certain cotangent bundles**

I will prove finiteness of the Hofer-Zehnder capacity of relatively compact neighborhoods of the zero section in cotangent bundles of closed manifolds M for which the map \pi_2(M)\to H_2(M;\mathbb{Z}) is nonzero. Joint work with Peter Albers and Urs Frauenfelder.

*Margherita Sandon:*

**Floer homology for translated points**

A point q in a contact manifold (M,\xi) is said to be a translated point of a contactomorphism \phi, with respect to a contact form \alpha for \xi, if it is a "fixed point modulo the Reeb flow", i.e. if q and \phi(q) are in the same Reeb orbit and \phi preserves \alpha at q. Translated points are key objects to look at when studying contact rigidity phenomena such as contact non-squeezing, orderability of contact manifolds and existence of bi-invariant metrics and quasimorphisms on the contactomorphism group. In my talk I will present a work in progress to construct a Floer homology theory for translated points of contactomorphisms and obtain a proof, under the assumption that the contact form \alpha has no closed contractible Reeb orbits, of a contact analogue of the Arnold conjecture on fixed points of Hamiltonian symplectomorphisms.

*Barney Bramham:*

**"Unlinked" Floer homology, and Poincaré surfaces**

A Poincaré surface can be a powerful tool for analysing a dynamical system in low dimensions. An interesting connection to pseudo-holomorphic curves was discovered in the late 90's by Hofer-Wysocki-Zehnder. But it remains difficult to construct the pseudo-holomorphic curves one would like to have. A natural way to over come this problem leads to a new version of Floer's Morse theory of the action functional in low dimensions, using unlinked collections of periodic orbits - a concept taken from LeCalvez' work on surface homeomorphisms. I will describe this "unlinked" Floer homology.