Jean-Philippe Lessard Department of mathematics 110 Frelinghuysen Road Hill Center Busch Campus Rutgers University Piscataway, NJ, 08854             Email: lessard@math.rutgers.edu Office: Hill 210 Phone number: (732) 445-2390 x7002 Vitae Research Statement

Positions

• NSF Mathematical Sciences Institutes Postdoctoral Fellowship.
  Selected by the Institute for Advanced Study (IAS) in Princeton and hosted by Rutgers University, 09/2009 - 07/2010.

• 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
  

• B.Sc. (Mathematics), Université de Sherbrooke, 2000.

Publications and Preprints

13) Rigorous computation of connecting orbits of dynamical systems, Part II. Homoclinic orbits of the Gray-Scott equation. In preparation, 2009.  With J.D. Mireles James.

12) Rigorous numerics for pattern formation models. In preparation, 2009. With Marcio Gameiro.

11) Rigorous computation of connecting orbits of dynamical systems, Part I. Finite elements, boundary value problem and parameterization of the manifolds. In preparation, 2009. With J.B. van den Berg, J.D. Mireles James and K. Mischaikow.

10) Existence of Secondary Bifurcations or Isolas for PDEs. Submitted, 2009. With Marcio Gameiro.

9) Rigorous Computation of Smooth Branches of Equilibria for the Three-Dimensional Cahn-Hilliard Equation. Submitted, 2009. With Marcio Gameiro.

8) A Priori Estimates and Validated Continuation for Equilibria of High Dimensional PDEs. Submitted, 2009. With Marcio Gameiro.

7) Recent Advances about the Uniqueness of the Slowly Oscillating Periodic Solutions of Wright's Equation. To appear in Journal of Differential Equations, 2009.

6) Global Smooth Solution Curves using Rigorous Branch Following.
To appear in Mathematics of Computation, 2009. With Jan Bouwe van den Berg and Konstantin Mischaikow.

5) Chaotic Braided Solutions via Rigorous Numerics: Chaos in the Swift-Hohenberg Equations.
    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 & Konstantin Mischaikow.

3) Validated Continuation for Equilibria of PDEs.
    SIAM Journal on Numerical Analysis, 45(4): 1398-1424 , 2007. With Sarah Day & 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. Uinversité 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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