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Nombre de programmes trouvés : 9004
Cours magistraux

le (1h10m42s)

Sylvain Maillot - An introduction to open 3-manifolds (Part 4)

W. Thurston's geometrization program has lead to manyoutstanding results in 3-manifold theory. Thanks to worksof G. Perelman, J. Kahn and V. Markovic, D. Wise, and I. Agol among others, compact 3-manifolds can now beconsidered to be reasonably well-understood.By contrast, noncompact 3-manifolds remainmuch more mysterious. There is a series of examples,beginning with work of L. Antoine and J. H. C. Whitehead,which show that open 3-manifolds can exhibit wildbehavior at infinity. No comprehensive structure theoryanalogous to geometrization à la Thurston is currently availablefor these objectsIn these lectures, we will focus on two aspects of the subject:(1) constructing interesting examples, and(2) finding sufficientconditions ...
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Cours magistraux

le (1h30m18s)

B. Weiss - Horocycle dynamics (Part 1)

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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Conférences

le (1h38s)

A. Lenzhen - Limit sets of Teichmuller geodesic rays in the Thurston boundary of Teichmuller space

H. Masur showed in the early 80s that almost every Teichmuller ray converges to a unique point in PMF. It is also known since a while that there are rays that have more than one accumulation point in the boundary.  I will give an overview of what is understood so far about the limit sets of Teichmuller rays, mentioning some recent progress. For example, I will mention recent joint work with K. Rafi and B. Modami where we give a construction of a ray whose limit set in PMF is a d-dimensional simplex.
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Conférences

le (54m22s)

I. Pasquinelli - Deligne-Mostow lattices and cone metrics on the sphere

Finding lattices in PU(n,1) has been one of the major challenges of the last decades.  One way of constructing a lattice is to give a fundamental domain for its action on the complex hyperbolic space.One approach, successful for some lattices, consists of seeing the complex hyperbolic space as the configuration space of cone metrics on the sphere and of studying the action of some maps exchanging the cone points with same cone angle.In this talk we will see how this construction can be used to build fundamental polyhedra for all Deligne-Mostow lattices in PU(2,1).
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Conférences

le (58m5s)

P. Apisa - Marked points in genus two and beyond

In the principal stratum in genus two, McMullen observed that something odd happens - there is only one nonarithmetic Teichmuller curve - the one generated by the decagon.  This strange phenomenon begets another - a primitive translation surface in genus two admits a periodic point that is not a Weierstrass point or zero only if it belongs to the golden eigenform locus. In this talk, we will explain how to leverage results of Mirzakhani-Wright to study the orbit closures of translation surfaces with marked points and sketch a proof of the previously mentioned result in genus two. We will also ...
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Conférences

le (1h3m20s)

S.Schleimer - An introduction to veering triangulations

Singular euclidean structures on surfaces are a key tool in the study of the mapping class group,of Teichmüller space, and of kleinian three-manifolds.  François Guéritaud, while studying work ofIan Agol, gave a powerful technique for turning a singular euclidean structure (on a surface) into atriangulation (of a three-manifold).  We will give an exposition of some of this work from the pointof  view  of  Delaunay  triangulations  for  theL∞-metric.   We  will  review  the  definitions  in  a  relaxedfashion,  discuss  the  technique,  and  then  present  applications  to  the  study  of  strata  in  the  space  ofsingular euclidean structures. If time permits, we will also discuss ...
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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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