Category Archives: Seminars and working groups

Friday, February 12

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Séminaire Teich : 11 h
Mario Shannon Will speak of the 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.

ASPI

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ASPI : Analyse spectrale et problèmes inverses Groupe de travail CPT-I2M
              (anciennement nommé GOMS)
This working group (formerly called GOMS, for Guides d’Ondes et Milieux Stratifiés) was created at the initiative of P. Duclos and Y. Dermenjian in 2003. Until the end of 2019 Michel Cristofol and Eric Soccorsi have been responsible for this working group. They are replaced in 2020 by

MEB

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The MEB (Mathematics, Evolution, Biology) seminar is organized by the
BioMath-Alea/SEM sub-team (from the former SEM team in 2017).
It is also the continuation of the MEG seminar of the former MMG (IML) and EM (LATP) teams
before the creation of the I2M.  As the team brings together mathematicians and biologists, the SEM seminar is interested in both modelling biological phenomena and processing their data.
The main theme of the seminar is biological evolution, and more broadly population biology
(population genetics and genomics, ecology, epidemiology, etc.).
But any presentation that falls within a team axis, or more generally interactions between
mathematics and biology are welcome.

Organiszer: Mikaël Kopp

Deterministic and Probabilistic Dynamical Systems

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This scientific project is in the domain of the probabilistic and statistical properties of dynamical
systems. We can identify two main axes of theoretical investigation which very often share questions,
methods and objectives.
•The first concerns deterministic dynamical systems
. In recent years efforts of mathematicians have been directed to study and understand systems beyond uniform hyperbolicity; notions of non-uniformly hyperbolic attractors, partially hyperbolic attractors, non-uniformly
expanding maps and flows have been introduced. These recent developments concern dynamical systems preserving a probability measure as well as dynamical systems preserving an infinite measure.
•The second deals with perturbations of deterministic system, which induces an additional source of randomness and allows us to define new models such as sequential dynamical systems, non-stationary, quenched and fibred dynamical systems, etc. In this context the proofs of limit theorems show new difficulties and call for new approaches and techniques or adaptations of previous methods.
Oganizer : Sandro Vaienti