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 onetoone 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 finitevolume 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. Le mardi 6 mai 2008 / Tuesday, May 6, 2008 16 h / 4:00 pm Université de Montréal Une réception suivra la conférence au Salon Mauricel'Abbé, Pavillon AndréAisenstadt (Salle 6245). There will be a reception after the lecture in Salon Mauricel'Abbé, Pavillon AndréAisenstadt (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 AndréAisenstadt 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 AndréAisenstadt, 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 AndréAisenstadt, 2920, ch. de la Tour Salle / Room 6214 