Jean-Philippe Lessard I have moved to Université Laval Here is a link to my webpage at Laval.

Positions

• Université Laval, Quebec City, Canada, (Assistant Professor), Aug. 2011 - Present.
  

• Basque Center for Applied Mathematica (BCAM), Bilbao, SPAIN (Group Leader of the research line Computational Mathematics) 08/2010 - 07/2011.

• NSF Mathematical Sciences Institutes Postdoctoral Fellowship.
  Selected by the Institute for Advanced Study (IAS) in Princeton and hosted by Rutgers University, 09/2009 - 08/2010.

• Rutgers University, Piscataway, USA (Postdoctoral Associate) Jan. 2008 - May 2008;  Jan. 2009 - Aug. 2009

• Vrije Universiteit Amsterdam, Netherland (Postdoctoral Researcher) Sept. 2007 - Dec. 2007;  June 2008 - Dec. 2008
  

Education

• Ph.D. (Mathematics), Georgia Institute of Technology, 2007. Advisor: Konstantin Mischaikow

• M.Sc (Mathematics), Université de Montréal, 2002. Advisor: Christiane Rousseau
  

Publications and Preprints

14) Rigorous numerics in Floquet theory: computing stable and unstable bundles of periodic orbits
Submitted, 2011. With Roberto Castelli.

13) Efficient rigorous numerics for high-dimensional PDEs via one-dimensional estimates
Submitted, 2011. With Marcio Gameiro.

12) Computational fixed point theory for differential delay equations with multiple time lags
Submitted, 2010. With Gábor Kiss.
      Here is a link containing relevant files associated to this work.

11) Rigorous numerics for symmetric connecting orbits: even homoclinics of the Gray-Scott equation
      SIAM Journal on Mathematical Analysis, 43 (4): 1557-1594, 2011. With J.B. van den Berg, J.D. Mireles James and K. Mischaikow.
      Here is a link containing relevant files associated to this work.

10) Existence of secondary bifurcations or isolas for PDEs
      Nonlinear Analysis: Theory, Methods and Applications, 74 (12): 4131-4137, 2011. With Marcio Gameiro.

9) Rigorous computation of smooth branches of equilibria for the three-dimensional Cahn-Hilliard equation
    Numerische Mathematik, 117 (4): 753-778, 2011. With Marcio Gameiro.

8) Analytic estimates and rigorous continuation for equilibria of higher-dimensional PDEs
    Journal of Differential Equations, 249 (9): 2237-2268, 2010. With Marcio Gameiro.

7) Global smooth solution curves using rigorous branch following
Mathematics of Computation, 79 (271), 1565-1584, 2010. With Jan Bouwe van den Berg and Konstantin Mischaikow.

6) Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright's equation
    Journal of Differential Equations, 248 (5): 992-1016, 2010.
Here is a link containing relevant files associated to this work.

5) Chaotic braided solutions via rigorous numerics: chaos in the Swift-Hohenberg equation
    SIAM Journal on Applied Dynamical Systems, 7 (3): 988-1031, 2008.  With Jan Bouwe van den Berg.

4) Validated continuation over large parameter ranges for equilibria of PDEs
    Mathematics and Computers in Simulation, 79 (4): 1368-1382, 2008. With Marcio Gameiro and Konstantin Mischaikow.

3) Validated continuation for equilibria of PDEs
    SIAM Journal on Numerical Analysis, 45(4): 1398-1424, 2007. With Sarah Day and Konstantin Mischaikow.

2) Validated continuation for infinite dimensional problems
    Ph.D. dissertation. Georgia Institute of Technology, 2007.

1) Bifurcations et chaos dans le système de Lorenz
    Master Thesis. Université de Montréal, 2002.

Mathematical Interests

• Dynamical Systems (PDEs, ODEs & Delay Equations)
  
• Rigorous Numerical Techniques
• Algebraic Topology & Topological Methods  (Conley Index Theory,  Morse Theory & Floer  Homology)
• Bifurcation Theory

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