The inscriptions are closed !
Mapping class groups of infinite type surfaces, also called
"big" mapping class groups, arise naturally in several dynamical
contexts, such as two dimensional dynamics, one dimensional complex
dynamics, "Artinization" of Thompson groups, etc.
In this
minicourse, we will present recent objects and phenomena related
to big mapping class groups. In particular, we will define two
faithful actions of some big mapping class groups. The first is an
action by isometries on a Gromovhyperbolic graph. The second is an
action by homeomorphisms on a circle in which the vertices of the
graph naturally embed. We will describe some properties of the
objects involved, and give some fruitful relations between the
dynamics of the two actions. For example, we will see that
loxodromic elements (for the first action) necessarily have
rational rotation number (for the second action). If time allows,
we will explain how to use these simultaneous actions to construct
non trivial quasimorphisms on subgroups of big mapping class
groups. This includes joint work with Alden Walker.
When studying the (nonsingular, C∞) 2dimensional foliations of 3manifolds (tangent to the boundary if any), those of T^2 × M , with M = [0, 1] or T^1 , which are transverse to the second factor play an important role. Such a foliation is determined, up to conjugacy, by its holonomy representation, which is an action of Z^2 on M , or, more simply, the data of a pair of commuting diffeomorphisms of M. The study of these objects and their possible deformations requires the understanding of centralizers of diffeomorphisms of M , which will be the main topic of this minicourse. In the case M = T^1, we will only consider diffeomorphisms without fixed points, since the other situation reduces to M = [0, 1]. In this second case, we will focus on diffeomorphisms without interior fixed points (to which one can reduce by subdivision), and actually on germs at 0 and 1, so that we will eventually consider M = R+. We will try to draw a parallel between the two situations (T^1 and R+) as follows :
No knowledge of the above works, even those often considered as classical (Denjoy, Herman, Yoccoz...) is assumed. We will, among other things, present the necessary background on diophantine approximation.
Mathieu and Sisto have introduced a novel method to study random walks on a large class of groups, socalled acylindrically hyperbolic groups (including for instance hyperbolc groups and mapping class groups). They can for instance prove the central limit theorem in this context. I will explain the general setting, several examples, and give the details of several (elementary!) proofs of their results.
Many wellstudied groups arise as groups of homeomorphisms of a
compact space that have a simple “local” behaviour, yet jointly
generate a complicated group. Examples include Thompson’s groups
and generalisations, groups of affine and projective interval
exchanges, topological full groups of minimal homeomorphisms, etc.
The notion of full group of a pseudogroup formalises this idea.
After reviewing some fundamental results in the theory of full
groups of pseudogroup, we will focus on their rigidity
properties.
En topologie, les théorèmes de classification sont ceux qu'on recherche
le plus; c'est l'objectif majeur; pouvoir classifier les objets
topologiques. On peut citer comme exemples le théorème de classification
surfaces, le théorème de LickorishWallace sur les 3 variétés obtenu par
chirurgie sur la sphère S^3...
Dans cet exposé, on parlera de collections de courbes remplissantes sur une
surface de genre g dont le complémentaire est un disque; on définira une
operation de chirurgie sur celles ci et on démontrera un théorème de
classification modulo cette opération.
The moduli space of abelian differential is endowed with a natural
foliation, whose leaves are locally described by varying the relative
periods, while fixing the absolute ones. The study of this foliation,
called the isoperiodic foliation, has been initiated in the 90’s by
Kontsevich and Eskin, and later by Calta and McMullen. It is since a
important tool in Teichmüler dynamics. However, it is only very recently
that results on the dynamics of its leaves have been obtained. In 2015
Hooper and Weiss gave the first examples of dense leaves (the ones through
the ArnouxYoccoz surfaces). Shortly after, Calsamiglia, Deroin,
Francaviglia obtaied a Ratnerlike classification of the minimal sets in
the principal stratum. Simultaneously, Hamenstädt obtained the ergodicity
for the MasurVeech measure in the same setting.
In this talk, after carefully defining the isoperiodic foliation, I will
give a criterion of density for leaves of the isoperiodic in rank 1 affine
manifolds. I will explain how this criterion can be used to discover new
dense leaves and new nontrivial minimal sets.
The two most basic families of examples of Anosov flows in dimension
three are the geodesic flows of hyperbolic surfaces and the suspension
flows generated by Anosov diffeomorphisms of the 2dimensional torus, both
fam ilies also called the algebraic Anosov flows. Nonalgebraic Anosov
flows where constructed for the first time in 1979 and 1980
(FranksWilliams for the nontransitive case and HandelThurston for the
transitive one) by the use of surgery procedures, which consists basically
in cut a 3manifold pos sessing some hyperbolic flow along incompressible
tori and then glue them back in a nontrivial way. Around the same time S.
Goodman described a surgery procedure where, given an Anosov flow and a
periodic orbit, it al lows to perform a Dehn surgery in a tubular
neighbourhood of this orbit and obtain a new manifold with a Anosov flow.
As a more sophisticated tool, in his 1983 work D. Fried proposed another
procedure to perform a Dehn surgery along a periodic orbit, which can be
interpreted a an infinitesimal version of the Goodman surgery. The main
advantage of the Fried’s proce dure with respect to the Goodman surgery is
that we can keep track of the topology of stable/unstable foliations of the
original flow during this surgery. The problem is that, although the new
flow preserves two 1dimensional fo liations for which the distance inside
the leaves are contracted/expanded by the positive/negative action of the
flow, it is not obvious that this flow is Anosov, the main problem being
related to check the differentiability and the exponential rates of
contraction/expansion. (The new flow is a so called topologically Anosov
flow.)
Our aim is to show the following:
Given an Anosov flow in a 3manifold, a Fried surgery along a
periodic orbit produces a flow which is topologically equivalent
to a (true) Anosov flow.
Date  Time  Event 

3
Monday
December, 2018

9:30  10:30 
Juliette Bavard

11:00  12:00 
Nicolás Matte Bon


14:00  15:00 
Hélène EynardBontemps


15:30  16:30 
Mario Shannon


4
Tuesday
December, 2018

9:30  10:30 
Sébastien Gouëzel

11:00  12:00 
Juliette Bavard


14:00  15:00 
Nicolás Matte Bon


15:30  16:30 
Olivier Glorieux


5
Wednesday
December, 2018

9:30  10:30 
Hélène EynardBontemps

11:00  12:00 
Sébastien Gouëzel


14:00  20:00 
Free afternoon


20:00  
Fondue evening


6
Thursday
December, 2018

9:30  10:30 
Nicolás Matte Bon

11:00  12:00 
Hélène EynardBontemps


14:00  15:00 
Juliette Bavard


15:30  16:30 
Abdoul Karim Sane


7
Friday
December, 2018

9:30  10:30 
Sébastien Gouëzel

11:00  12:00 
Florent Ygouf

The conference will take place at Centre Paul Langevin.
It will provide full board accomodation (mostly in double rooms).
The number of participants is limited to 25. We will give the priority to PhD students and postdocs.
To register for the conference, please contact one of the organisers:
If you need financial support for your travel expenses, please include an estimate of the cost, we will reimbourse it depending on the available fundings.
The closest train station is in Modane. From there it is a 20 km taxi ride to the hotel.