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Cours magistraux

le (1h1m22s)

A. Wright - Mirzakhani's work on Earthquakes (Part 3)

We will give the proof of Mirzakhani's theorem that the earthquake flow and Teichmuller unipotent flow are measurably isomorphic. We will assume some familiarity with quadratic differentials, but no familiarity with earthquakes, and the first lecture will be devoted to preliminaries. The second lecture will cover the proof, and the final lecture additional connections such as the link between Weil-Petersson and Masur-Veech volumes. If time allows, we will mention Mirzakhani's recent result on counting mapping class group orbits, which relies on her work on earthquake flow.
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Cours magistraux

le (1h11m55s)

A. Zorich - Counting simple closed geodesics and volumes of moduli spaces (Part 3)

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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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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Cours magistraux

le (1h2m15s)

J. Smillie - Horocycle dynamics (Part 2)

A major challenge in dynamics on moduli spaces is to understand the behavior of the horocycle flow. We will motivate this problem and discuss what is known and what is not known about it, focusing on the genus 2 case. Specific topics to be covered include:* SL_2(R) orbit closures and invariant measures in genus 2.* Quantitative nondivergence.* The structure of minimal sets.* Rel and real-rel, and their interaction with the horocycle flow* Horizontal data diagrams and other invariants for horocycle invariant measures.* Classification of measures and orbit-closures in the eigenform loci.* Recent and not-so-recent examples of unexpected measures and orbit-closures.
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Cours magistraux

le (1h11m31s)

A. Wright - Mirzakhani's work on Earthquakes (Part 2)

We will give the proof of Mirzakhani's theorem that the earthquake flow and Teichmuller unipotent flow are measurably isomorphic. We will assume some familiarity with quadratic differentials, but no familiarity with earthquakes, and the first lecture will be devoted to preliminaries. The second lecture will cover the proof, and the final lecture additional connections such as the link between Weil-Petersson and Masur-Veech volumes. If time allows, we will mention Mirzakhani's recent result on counting mapping class group orbits, which relies on her work on earthquake flow.
Voir la vidéo

 
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