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Cours magistraux

le (1h12m0s)

A. Zorich - Counting simple closed geodesics and volumes of moduli spaces (Part 2)

In  the  first two lectures I will try to tell (or, rather, to  give  an  idea)  of  how  Maryam Mirzakhani has counted simple  closed  geodesics on hyperbolic surfaces. I plan to briefly  mention her count of Weil-Peterson volumes and her proof of Witten's conjecture, but only on the level of some key ideas.In the last lecture I plan to show how ideas of Mirzakhani work in counting problems related to flat surfaces, namely, in computation of Masur-Veech volumes and in counting meanders.
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Conférences

le (57m36s)

C. Judge - Systoles in translation surfaces

I will discuss joint work with Hugo Parlier concerning the shortest noncontractible loops—’systoles’—in a translation surface. In particular, we provide estimates (some sharp) on the number of systoles (up to homotopy) in the strata H(2g-2) and the stratum H(1,1).  We also determine the maximum systolic ratio (length squared/area) in H(2g-2), and we give a conjectural value for maximum systolic ratio in H(1,1).
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Conférences

le (57m17s)

R. Santharoubane - Quantum representations of surface groups

I will show how we can produce exotic representations of surface groups from the Witten-Reshetikhin-Turaev TQFT. These representations have infinite images and give points on character varieties that are fixed by the action of the mapping. Moreover we can approximate these representations by representations into finite groups in order to build exotic regular finite covers of surfaces. These covers have the following property: the integral homology is not generated by pullbacks of simple closed curves on the base. This is joint work with Thomas Koberda.
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Conférences

le (1h3m54s)

A. Wright - Nearly Fuchsian surface subgroups of finite covolume Kleinian groups

Multicurves have played a fundamental role in the study of mapping class groups of surfaces since the work of Dehn. A beautiful method of describing such systems on the n-punctured disk is given by the Dynnikov coordinate system.  In this talk we describe polynomial time algorithms for calculating the number of connected components of a multi curve, and the geometric intersection number of two multicurves on the n-punctured disk, taking as input their Dynnikov coordinates.  This is joint work
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Cours magistraux

le (1h4m44s)

J. Aramayona - MCG and infinite MCG (Part 2)

The first part of the course will be devoted to some of the classicalresults about mapping class groups of finite-type surfaces. Topics may include: generation by twists, Nielsen-Thurston classification,abelianization, isomorphic rigidity, geometry of combinatorial models.In the second part we will explore some aspects of "big" mapping class groups, highlighting the analogies and differences with their finite-type counterparts, notably around isomorphic rigidity, abelianization, and geometry of combinatorial models.
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Cours magistraux

le (1h28m28s)

J. Aramayona - MCG and infinite MCG (Part 3)

The first part of the course will be devoted to some of the classical results about mapping class groups of finite-type surfaces. Topics may include: generation by twists, Nielsen-Thurston classification, abelianization, isomorphic rigidity, geometry of combinatorial models. In the second part we will explore some aspects of "big" mapping class groups, highlighting the analogies and differences with their finite-type counterparts, notably around isomorphic rigidity, abelianization, and geometry of combinatorial models.
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Conférences

le (53m9s)

D. Davis - Periodic paths on the pentagon

Mathematicians have long understood periodic trajectories on the square billiard table. In the present work, we describe periodic trajectories on the regular pentagon – their geometry, symbolic dynamics, and  group  structure.   Some  of  the  periodic  trajectories  exhibit  a  surprising  "dense  but  not  equidistributed" behavior.  I will show pictures of periodic trajectories, which are very beautiful.  This is joint work with Samuel Lelièvre and Barak Weiss.
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