Vendredi 26 février, à 11h,
Khaydar Nurligareev nous parlera des contages combinatoires des différents objets, notamment, des surfaces à petits carreaux.
Le thème sera :
Probabilité d’être irréductible
Asymptotics for the probability of labeled objects to be irreducible
There are a number of combinatorial structures that admit, in a broad sense, a notion of irreducibility, including connected graphs and surfaces, irreducible tournaments, indecomposable permutations and so on. We are interested in the probability that a random labeled object is irreducible, as its size tends to infinity. We will show that for some classes of objects it is possible to obtain the asymptotics for these probabilities in a common manner and that asymptotic coefficient have a combinatorial meaning. More precisely, it is so when the considered combinatorial class can be described as a set or a sequence of the corresponding irreducible class, and its counting sequence grows sufficiently fast. Moreover, we will show how to obtain the asymptotic probability that a random labeled object has a given number of irreducible components, and we will indicate the combinatorial meaning of the coefficients involved in the asymptotic expansions.
This is an ongoing work joint with Thierry Monteil.
Vendredi 12 février : 11 h
Mario Shannon parlera des iModèles hyperboliques des flots topologiques d’Anosov transtitifs.
Hyperbolic models of transitive topological Anosov flows.
A topological Anosov flow on a closed 3-manifold is a non-singular flow that resembles very much a smooth Anosov flow: It is expansive and satisfies the (global) shadowing property. Moreover, it preserves a pair of transverse sta- ble/unstable foliations that intersect along the orbits of the flow. The main difference with a (smooth) Anosov flow is the lack of a global uniformly hyper- bolic structure.
We investigate the question of weather or not every topological Anosov flow in a 3-manifold is, actually, orbit equivalent with some smooth Anosov flow. Apart from its own theoretical interest, this question appears related with some techniques for the construction of Anosov flows on 3-manifolds, notably with the so called Fried surgery.
Our work consists in show that, under the hypothesis of transitivity, every topological Anosov flow is orbitally equivalent with a smooth Anosov flow.
In this talk we are going to present the main ideas and difficulties behind the construction of these smooth hyperbolic models associated with transitive topological Anosov flows. As well, we will give a flavour of how this study can be reduced to pseudo-Anosov dynamics on surfaces with boundary.