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Frederic CHARDARD's web page


I am agrégé-préparateur (a job similar to an assistant-professor position) at UMPA, the laboratory of mathematics of ENS Lyon. I work on the stability of solitary waves. 		Photo of Frederic Chardard

Coordinates

Office address

Frédéric Chardard (Office 430 South)
UMPA
ENS de Lyon (Site Sciences)
46, allée d'Italie
69007 Lyon
France

Office phone

33+4 72 72 81 88

Fax

33+4 72 72 84 80

Cell phone

33+ 6 74 40 29 32

Email

firstname.lastname at ens-lyon.fr

Curriculum Vitae

Long version

  • Born in 1982.
  • Single person without children.

Degrees

  • 2005-2009: PhD at CMLA ( ENS Cachan ) on the stability of solitary waves. PhD advisor: Frédéric DIAS .
  • 2005: Master of Science on Partial Differential Equations and Scientific Calculus at Paris-Sud XI Orsay.
  • 2003: Bachelor of science on Mathematics (Paris-Sud XI Orsay).
  • 2000: High school diploma (Baccalauréat scientifique spécialité Mathématiques).

Employment

  • Since 2009: Agrégé-Préparateur at ENS Lyon.
  • 2006-2009: PhD Grant and Teaching Assistant (Allocataire-moniteur).
  • 2002-2006: Pupil of ENS Cachan.

Teaching:

  • 2009-: Tutorials on Differential Calculus, Topology, Numerical Analysis. Short course on Differential Geometry.
  • 2006-2009: Tutorials on Finte Differences/Finte Elements/Finite Volumes and Numerical Linear Algebra.
  • 2003-2006: 120 hours of oral interrogations.

PhD thesis

I defended on Friday, May 15th, 2009 at ENS Cachan.

PhD dissertation

Abstract of the thesis

Stability of solitary waves

This thesis is devoted to the stability of solitary waves, and more precisely to the applications of the Maslov index to the spectral stability problem. We show how the stability problem can be related to a family of linear Hamiltonian ODE. It is then possible to define a Maslov index for periodic waves and solitary waves. We compute the limit, when it exists, of the Maslov index of a sequence of periodic waves which converges to a solitary wave. We describe how exterior algebra can be used to compute the Maslov index, both in the periodic and solitary wave cases. We then use this framework for solitary waves and periodic waves arising in the Kawahara equation and for solitary waves arising in a longwave-shortwave interaction system. Lastly, we deal with the stability of stationary solutions of a model for flows over a non-uniform bottom by using a slightly different method.

Committee

Thomas J. BRIDGES, Professor, Surrey, United Kingdom
Frédéric DIAS, Professor, ENS Cachan
Christopher K.R.T. JONES, Professor, University of North Carolina at Chapel Hill, USA
Juan-Pablo ORTEGA, Chargé de recherches, CNRS
Jean-Claude SAUT, Professor, Paris XI
Nikolay TZVETKOV, Professor, Lille I

Publications

F.Chardard, F.Dias, T.J.Bridges. Computing the Maslov index of solitary waves. Part 2:Phase space with dimension greater than four, Physica D. 240 1334-1344 (2011).
PDF doi:10.1016/j.physd.2011.05.014

F.Chardard, F.Dias, H.-Y. Nguyen, J.-M. Vanden-Broeck. Stability of some stationary solutions to the forced KdV equation with one or two bumps, Journal of Engineering Mathematics 70 175-189 (2011).
PDF doi: 10.1007/s10665-010-9424-6

F.Chardard, F.Dias, T.J.Bridges. On the Maslov index of multi-pulse orbits, R. Soc. Lond. Proc. Ser. A 465  2897-2910 (2009).
PDF, doi: 10.1098/rspa.2009.0155

F.Chardard, F.Dias, T.J.Bridges. Computing the Maslov index of solitary waves. Part 1: Hamiltonian systems on a 4−dimensional phase space, Physica D 238  1841-1867 (2009).
See "Computational aspects of the Maslov index of solitary waves" for the long version of this article.
doi:10.1016/j.physd.2009.05.008

F.Chardard. Maslov index for solitary waves obtained as a limit of the Maslov index for periodic waves, C. R. Acad. Sci. Paris, Ser. I 345/12  689-694 (2007).
PDF, doi:10.1016/j.crma.2007.11.003

F.Chardard, F.Dias, T.J.Bridges. Fast computation of the Maslov Index for hyperbolic linear systems with periodic coefficients, Journal of Physics A : Mathematical and General 39  14545-14557 (2006)
PDF doi:10.1088/0305-4470/39/47/002

Submitted article:

T.J.Bridges, F.Chardard. Transversality of homoclinic orbits, the Maslov index, and the symplectic Evans function, submitted to Ann. Inst. H. Poincaré Anal. Non Linéaire
PDF

Preprints:

F.Chardard, F.Dias, T.J.Bridges. Computational aspects of the Maslov index of solitary waves, hal-00383888.

Un soliton