Prochainement

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Jeudi 19 avril 14:00-15:00 Boris Hasselblatt  (Tufts University)
New contact flows on 3-manifolds

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Lieu : IMO, salle 2L8

Résumé : Foulon-Ding-Geiges-Handel-Thurston surgery produces contact flows that are unusual and interesting in several ways. The periodic fiber flow in the unit tangent bundle becomes parabolic or even hyperbolic, and the geodesic flow becomes a nonalgebraic contact Anosov flow with larger orbit growth. Recent work by Bishop, Hughes, Vinhage and Yang promises a quantification of the gap between the Liouville and topological entropies.

Notes de dernières minutes : Café culturel assuré à 13h par Anne Vaugon

New contact flows on 3-manifolds  Version PDF

Jeudi 12 avril 14:00-15:00 Sébastien Miquel  (Laboratoire de Mathématique d'Orsay)
Arithméticité de sous-groupes contenant un réseau horosphérique

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Lieu : IMO, salle 2L8

Résumé : Si G est un groupe simple de rang au moins 2 et P un sous-groupe parabolique de G, Margulis a conjecturé que tout sous-groupe discret, Zariski-dense de G intersectant le radical unipotent de P en un réseau est un réseau arithmétique de G. Au travers de deux exemples, je présenterai une preuve de cette conjecture qui utilise des travaux de G. Margulis, H. Oh et le théorème de Ratner.

Notes de dernières minutes : Café culturel assuré à 13h par Yves Benoist

Arithméticité de sous-groupes contenant un réseau horosphérique  Version PDF

Jeudi 5 avril 14:00-15:00 Warwick Tucker  (Uppsala University and Collegium de Lyon)
Computer-assisted proofs in Dynamical Systems

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Lieu : IMO, salle 2L8

Résumé : In this talk, we will describe some problems taken from the field of Dynamical Systems, and show how they were successfully solved by computer-assisted proofs. Although the mathematical techniques used when solving these problems vary a lot, the computational parts all share a common foundation : interval analysis. We will give a short introduction to this field of computing, and see how it was applied to help solve the presented problems. The mathematics specific to each problem will also be discussed.

Notes de dernières minutes : Café culture assuré à 13h15 par Marc Mezzarobba (LIP 6)

Computer-assisted proofs in Dynamical Systems  Version PDF

Jeudi 29 mars 14:00-15:00 Rhiannon Dougall  (Université de Nantes)
Critical exponents for normal subgroups

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Lieu : Institut de Mathématique d’Orsay, salle 2L8

Résumé : Fix a cocompact group 𝚪_0 of isometries of a negatively curved, simply connected space X. We are interested in the dynamics of its normal subgroups 𝚪. Namely, we study the critical exponent 𝛅(𝚪), which is the exponential growth rate of the 𝚪-orbit of a point. We characterise the existence of a gap 𝛅(𝚪) < 𝛅(𝚪_0) uniform in a family of normal subgroups 𝚪, in terms of permutation representations given by the quotients 𝚪_0/𝚪.
The proof uses the symbolic dynamics for the geodesic flow, for which we obtain the analogous statements for countable state shifts obtained as group extensions of a finite state shift.

Notes de dernières minutes : Café culturel à 13h par Damien Thomine.

Critical exponents for normal subgroups  Version PDF

Jeudi 22 mars 14:00-15:00 Andres Koropecki  (Universidade Federal Fluminense (Brésil))
Prime ends and boundary dynamics for surface homeomorphisms

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Lieu : Institut de Mathématique d’Orsay, salle 2L8

Résumé : I will talk about a joint work with P. Le Calvez and M. Nassiri which relates the dynamics of a planar homeomorphism in the boundary of a simply connected open invariant set U with the corresponding dynamics induced in Carathéodory’s prime ends compactification of U. I will focus in the case where the prime ends rotation number is rational and the dynamics area-preserving, in which case we obtain a description of the dynamics very similar to what happens in the circle, as well as strong restrictions on the topology of the boundary of U.

Notes de dernières minutes : Café culturel à 13h par Sylvain Crovisier.

Prime ends and boundary dynamics for surface homeomorphisms  Version PDF

Jeudi 15 mars 14:00-15:00 David Kerr  (Texas A&M University)
Almost finiteness and the small boundary property

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Lieu : IMO, salle 2L8

Résumé : The notion of almost finiteness for group actions on compact spaces is an analogue both of hyperfiniteness in the setting of measure-preserving actions and of Z-stability in the setting of C*-algebras and is related to dynamical comparison in a way that is reminiscent of the link between Z-stability and strict comparison in the Toms-Winter conjecture. I will explain how this relationship with dynamical comparison can be illuminated by means of the small boundary property and the concept of almost finiteness in measure, leading to new classification results for crossed product C*-algebras. This is joint work with Gabor Szabo.

Notes de dernières minutes : Café culturel à 13h par Amaury Freslon

Almost finiteness and the small boundary property  Version PDF

Jeudi 8 mars 14:00-15:00 Mladen Bestvina  (University of Utah)
The Farrell-Jones conjecture for free-by-cyclic groups

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Lieu : IMO, salle 2L8

Résumé : The Farrell-Jones conjecture for a given group is an important conjecture in manifold theory. I will review some of its consequences and will discuss a class of groups for which it is known, for example 3-manifold groups. Finally, I will discuss a proof that free-by-cyclic groups satisfy FJC, answering a question of Lück. This is joint work with Koji Fujiwara and Derrick Wigglesworth.

Notes de dernières minutes : Café culturel à 13h par Frédéric Paulin

The Farrell-Jones conjecture for free-by-cyclic groups  Version PDF