# ICMAT Laboratory "Viktor Ginzburg" : planned activities

Tuesday, June 2, 2015

Hamiltonian Dynamics Day

Place: Aula Gris 1 - ICMAT, Campus de Cantoblanco, Madrid (Spain)

10:00 Francisco Javier Torres de Lizaur

Title: "Knotted structures in high-energy Beltrami fields on the torus and the sphere"

Abstract: Beltrami fields on a three dimensional manifold are eigenfields of the curl operator. They describe the flow of an ideal fluid whose vorticity and velocity are proportional at every point. If they are everywhere non zero, they can also be seen as the Reeb field of a contact form. We show that on the sphere and on the torus high energy Beltrami fields can exhibit arbitrarily complicated topological behavior. More precisely, let S be a finite collection of (pairwise disjoint, but possibly knotted and linked) closed curves and tubes in the round sphere S3 or the flat torus T3 . In the case of the torus, we assume that S is contained in a contractible subset. For any sufficiently large integer ? there exists a diffeomorphism $$\Phi$$ of S3 or T3 and a Beltrami field u satisfying $$\nabla u = \lambda u$$ such that $$\Phi$$(S) is a union of vortex lines and vortex tubes of $$u$$.

12:00 Roger Casals

Title: "Criteria for overtwistedness"

Abstract: 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.

15:30 Basak Gurel

Title: "Hyperbolic fixed points and periodic orbits in Hamiltonian dynamics"

Abstract:

Past activities

Friday, February 22, 2013

12:00 :  Viktor Ginzburg's lab Opening Lecture "Periodic orbits of Hamiltonian systems"

VIKTOR GINZBURG, University of California at Santa Cruz

Place: ICMAT, Campus de Cantoblanco, Madrid (Spain)

Thursday, May 23, 2013

10:30 Yasha Savelyev (Université de Montréal, Centre de recherches mathématiques)

Title: Virtual Morse theory revisited

Abstract: There is an interesting phenomenon in Hofer geometry which states roughly that the Hofer length functional behaves virtually like a perfect Morse-Bott functional, with a meaningful Morse theory. Originally this appeared in a rather limited context and was somewhat overlooked. We present a generalization of this phenomenon for all (monotone) symplectic manifolds.

12:00 Basak Gurel (Vanderbilt University)

Title: Action-index relations for Hamiltonian dynamical systems

Abstract: In this talk, we will discuss a rigidity feature for Hamiltonian diffeomorphisms with finitely many periodic orbits. Namely, we show that, under suitable assumptions on the ambient manifold, the actions and mean indices of periodic orbits of such a diffeomorphism must satisfy certain relations. This talk is based on joint work with Mike Chance and Viktor Ginzburg.

15:00 Roger Casals (ICMAT)

Title: A Remark on the Reeb flow for spheres

Abstract: We prove the non--triviality of the Reeb flow for the standard contact spheres

$$S^{2n+1}$$, $$n\neq3$$, inside the fundamental group of their contactomorphism group. The argument uses the existence of homotopically non--trivial $$2$$--spheres in the space of contact structures of a $$3$$--Sasakian manifold.

Monday, May 27, 2013

12:30:  Displacement points in contact geometry

YASHA SAVELYEV, Université de Montréal, Centre de recherches mathématiques

Place: ICMAT, Campus de Cantoblanco, Madrid (Spain)

Wednesday, 23rd October

11:30 : HAM Seminar-Course, Aula Gris 1, ICMAT

YAKOV SAVELYEV,  ICMAT
"The Hofer metric of the group of Hamiltonian diffeomorphisms I"

Wednesday, 30th October

11:30 : HAM Seminar-Course, Aula Gris 1, ICMAT

YAKOV SAVELYEV,  ICMAT
"The Hofer metric of the group of Hamiltonian diffeomorphisms II"

November 11-15, 2013

CRM-ICMAT Conference Symplectic aspects of Dynamical Systems
(this conference is also a closing activity for the CRM RP Geometry and Dynamics of integrable systems)

Place: ICMAT, Campus de Cantoblanco, Madrid (Spain)

June 2-6, 2014

Workshop GESTA 2014

Place: ICMAT, Campus de Cantoblanco, Madrid (Spain)

July 14-18, 2014

Place: ICMAT, Campus de Cantoblanco, Madrid (Spain)