CRM Research Program on Geometric Flows and Equivariant Problems in Symplectic Geometry

 Seminar on Symplectic and Poisson Geometry

Takes place on Thursdays following the following schedule

Place: Big room of CRM
Morning session 1130-1230
Afternoon session 1500-1600

(from 11 on, there will be cookies and coffee in front of the conference room)

Exceptions for the second week of April when we also have sessions on Monday and Tuesday (see the schedule below for details)



June 2008

June 5, Thursday

11:30 am: Boris Khesin (University of Toronto), Pseudo-Riemannian geodesics and billiards

In pseudo-Riemannian geometry the spaces of space-like and time-like geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. Furthermore, the space of all geodesics has a structure of a Jacobi manifold. In the talk I will describe the geometry of these structures, define pseudo-Euclidean billiards and discuss their properties. In particular, I will outline complete integrability of the billiard in the ellipsoid and the geodesic flow on the ellipsoid in pseudo-Euclidean space; these results are pseudo-Euclidean counterparts to the classical theorems of Euclidean geometry that go back to Jacobi and Chasles/.
/It turns out that contact integrability in the problem leads to a Poncelet-type
result for light-like geodesics on the ellipsoid.

15:00 pm: Francisco Presas (CSIC, Madrid), Holomorphic Engel structures

   We outline the classification of Engel structures (completely non-integrable dimension 2 distributions on a 4-fold) in the complex case. The proof relies on some constraints to the positivity in a holomorphic non-integrable distribution coming for Demailly's work and some results about the existence of compact leaves for holomorphic foliations.



June 13, Friday, Special CRM thematic day "New Trends in Poisson Geometry"



June 16-June 21, GAP VI, Geometry and Physics (Integrable Systems)

minicourses by

Yves Colin de Verdière, Institut Fourier, Semi-classical Analysis of Integrable systems


Johannes Duistermaat, Universiteit Utrecht, QRT and elliptic surfaces


Hakan Eliasson, Institut de Mathématiques de Jussieu, KAM for the non-linear Schröndinger equation.


San Vu Ngoc, Université de Rennes, Sympletic invariants of integrable Hamiltonian systems.


for details look at the webpage of GAP VI.


On Wednesday 18 there will be a talk of the seminar at 3pm.

This schedule is compatible with the schedule of GAP.


Wed 18, 15pm- Adrian Ocneanu (PennState University)

Higher root systems

We describe the construction of root systems of simple Lie groups
from the quantum subgroups of SU(2), e.g. the icsoahedral subgroup of
SU(2) leads to the Lie group of type E_8.

 From the quantum subgroups of SU(3) and SU(4),which we classify, we
obtain higher root systems. We describe topological and combinatorial
interpretations of the higher roots, which fit into a program of
constructing QFT models in a physical number of dimensions.

The usual Chebyshev polynomials are associated to representations of
SU(2). Using the higher root systems, we introduce generalizations of
Chebyshev polynomials to any root system and find their generating


June 25- June 28, Conference on Moment Maps. Look at the webpage for the programme.