On Slow-Fast Dynamics: Theory, Numerics, Application to Life and Earth Sciences

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Workshop
From June 03, 2013
to June 07, 2013

Objectives

Theoretical research in singular perturbation theory advances rapidly and in many directions. Planar slow-fast systems, although quite well-understood, still encompass a number of open questions such as the location and distribution of isolated periodic orbits. In higher dimensional systems, slow-fast vector fields give rise to even richer dynamics, in particular, complex oscillations such as Mixed-Mode Oscillations (MMOs) and bursting oscillations. Important theoretical challenges are concerned with the questions of more than two time scales, complex patterns of oscillations with more than four variables, the effect of time scales on stochastic systems, spatially extended systems, large-scale systems, etc.. The question of various model reductions is central to these challenges. 
Application areas where multiple time scales play an important role are numerous, especially in the life sciences. Observing and modelling real-world processes as diverse as the electrical activity of neuron cells, chemical reactions, turbulent flows or (some aspects of) the climate, often involves multi-scale data and the development of mathematical models that incorporate these different time and space scales, which may or may not be explicit. From the experimental data to the mathematical model, identifying the time scales is a fundamental challenge, and according to the process under study, the knowledge of these time scales is very variable and system-dependent. Developing mathematical techniques that do not depend on an explicit timescale separation is also an important challenge to bridge the gap between theory and applications. 
In this workshop, a panorama of current research in slow-fast dynamics will be presented, both at theoretical and computational level and also with a clear view towards applications, in particular in neuroscience and climate modelling (in link with the worldwide initiative mpe2013). World leading experts will give keynote lectures on the aforementioned topics; remaining talks will be shorter and will focus on current research questions in this field. We hope to bring together different communities (theoretical, computational, experimental), all interested in multiple time scale dynamics, hence fostering discussion, interaction and promoting new collaborations. Also, we wish to discuss during the workshop the possibility of creating an international network for research in slow-fast dynamics; in particular, such a network will allow this type of meeting to be recurrent.

Scientifc Committee

Eric Benoît, University of La Rochelle
Freddy Dumortier, University of Hasselt
Jean-Pierre Françoise, University Pierre & Marie Curie- Paris 6
Boris Gutkin, École Normale Supérieure de Paris
Jean-Christophe Poggiale, Université de Marseille
Robert Roussarie, Université de Dijon

Organizers

Peter De Maesschalck, University of Hasselt
Mathieu Desroches, INRIA
Mark Kramer, Boston University
Martin Krupa, INRIA
Serafim Rodrigues, University of Plymouth
Alexandre Vidal, University of Evry
Haiping Zhu, University of York

List of participans

A. Rod Gover
Ali Maalaoui
Alice Chang
Andreas Juhl, Uppsala Universitet
Andreas Juhl Humbold, t Universität zu Berlin
Antonio Ache,  Princeton University
Azahara de la Torre Pedraza,  Universitat Politècnica de Catalunya
Bo XIA,  Université Paris-Sud
Charles Fefferman,  Princeton University
Christian Murray,  University of Cape Town
Daniel Sánchez Taltavull,  Centre de Recerca Matemàtica
Dung Nguyen Thac
Gabjin Yun,  Myongji University
Guglielmo Albanese , Università degli studi di Milano
hassan jaber,  Institut Élie Cartan
Heiko Gimperlein
Ilaria Mondello,  Université de Nantes
Janine Bachrachas,  Peterburg McGill University
Janine Bachrachas
Javier Saenz Casas,  Centro de investigación en Matemáticas de México
Jeffrey Case Princeton University
Jesús Pérez García
Jie Qing University of California at Santa Cruz
Jih-Hsin Cheng,  Institute of Mathematics – Academia Sinica
Jingyang Zhong,  University of California at Santa Cruz
Joaquin Pérez , Universidad de Granada
Jose Luis Teruel Carretero,  Universidad de Granada
Kengo Hirachi,  The University of Tokyo
Kostiantyn Drach
Laurent Hauswirth,  Université Paris-Est Marne-la-Vallée
Luca Martinazzi , Rutgers University
Luis Guijarro Santamaria,  Universidad Autónoma de Madrid
Luis López Rios,  Universidad de Chile
Marcin Styborski
Maria del Mar González,  Universitat Politècnica de Catalunya
Matteo Cozzi
Matthew Gursky,  University of Notre Dame
Mircea Petrache,  ETH Zürich
Murray Christian,  University of Cape Town
Nguyen Thac Dung,  National Tsing Hua University
Nick Reichert,  Princeton University
Niels Martin,  Princeton University
Nobuhiko Otoba
Patrick Munroe
Paul Yang
Raul Quiroga Barranco,  Centro de investigación en Matemáticas de México
Ray Yang Courant,  Institute of Mathematical Sciences
Ridha Yacoub
Robert Kusner,  University of Massachusetts at Amherst
Robin Graham
Rod Gover,  University of Auckland
Saikat Mazumdar,  Institut Élie Cartan
Sameerah Jamal,  University of the Witwatersrand
Seongtag Kim, Inha University
Seungsu Hwang
Spyros Alexakis, University of Toronto
Stephen McKeown, University of Washington
Taiji Marugame, Taiji Marugame
Vicent Gimeno Garcia, Universitat Jaume I
Wang Yi, Stanford University
William Meeks III, University of Massachusetts at Amherst
Xia Bo, Université Paris-Sud
Xue Hu, The Chinese Academy of Sciences
Yoshihiko Matsumoto, The University of Tokyo
Yuxim Ge, Université Paris Est Créteil
Zisis Sakellaris

List of keynote speakers

Freddy Dumortier, Hasselt University, Belgium
Jean-Pierre Françoise, Pierre & Marie Curie University
Olivier Faugeras, INRIA Sophia Antipolis
G. Bard Ermentrout, University of Pittsburgh
Antoni Guillamon, UPC
John Guckenheimer, Cornell University
Tasso J. Kaper, Boston University
Yannis Kevrekidis, Princeton University
Martin Wechselberger, University of Sydney
Antonios Zagaris, University of Twente, The Netherlands​

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