Chaire Aisenstadt 2008 Aisenstadt Chair
Professor Jean Christophe Yoccoz
(Collège de France)

Une série de conférences / A series of lectures
DIAPORAMA DE LA CONFÉRENCE/LECTURE SLIDESHOW

Dynamics and Geometry of Interval Exchange Maps and Translation Surfaces

An interval exchange map (iem) is a one-to-one map of the interval which is locally a translation except at finitely many discontinuities; the simplest example of such maps are rotations on a circle (cut at some point to get an interval). To analyze the dynamics of such transformations, Rauzy, Veech and Zorich have developped a renormalization algorithm which generalizes the classical continuous fraction for irrational numbers. In some ways, iems are similar to rotations; for instance, almost all iems are uniquely ergodic (Masur, Veech); on the other hand, almost all iems with nonrotational combinatorics are weakly mixing, so quite different in this respect from rotations. Taking the suspension of an iem one gets a translation surface; this remarkable geometric object can also be seen as a Riemann surface equipped with a holomorphic one form. The Teichmüller space and the moduli space for these surfaces are of special interest. In particular the moduli space is a complex finite-volume orbifold equipped with an action of SL(2,R), the restriction to the diagonal subgroup giving rise to a flow called the Teichmüller flow. The first lecture will give a general overview of the subject, aimed at a general scientific audience, stressing ideas rather than precise mathematical statements. The following three will deal with some of the recent developments of this very active subject.

Cette conférence s'adresse à un large auditoire.
This lecture is suitable for a general audience.

Le mardi 6 mai 2008 / Tuesday, May 6, 2008

16 h / 4:00 pm

Université de Montréal
Pavillon André-Aisenstadt, 2920, ch. de la Tour
Salle / Room 1140

Une réception suivra la conférence au Salon Maurice-l'Abbé, Pavillon André-Aisenstadt (Salle 6245).

There will be a reception after the lecture in Salon Maurice-l'Abbé, Pavillon André-Aisenstadt (Room 6245).


Dynamics and geometry of Interval Exchange Maps and Translation Surfaces - Interval Exchange Maps

Le mercredi 7 mai 2008 / Wednesday, May 7, 2008

11 h / 11:00 am

 

Université de Montréal, Pavillon André-Aisenstadt

2920, ch. de la Tour

Salle / Room 6214


Dynamics and Geometry of Interval Exchange Maps and Translation Surfaces - Translation Surfaces

Le jeudi 8 mai 2008 / Thursday, May 8, 2008

11 h / 11:00 am

 

Université de Montréal

Pavillon André-Aisenstadt, 2920, ch. de la Tour

Salle / Room 6214


Dynamics and Geometry of Interval Exchange Maps and Translation Surfaces - Moduli Space and the Teichmüller Flow

Le vendredi 9 mai 2008 / Friday, May 9, 2008

11 h / 11:00 am

 

Université de Montréal

Pavillon André-Aisenstadt, 2920, ch. de la Tour

Salle / Room 6214