Frédéric Paquin-Lefebvre

Je suis chercheur postdoctoral à l'École Normale Supérieure de Paris, membre du Laboratoire de Mathématiques Appliquées et Biologie Computationnelle de David Holcman. J'ai récemment soutenu une thèse à l'Université de la Colombie-Britannique sur l'analyse de structures spatio-temporelles dans les équations de réaction-diffusion, sous la direction de Michael J. Ward et Wayne Nagata. J'ai aussi travaillé avec le Professeur Jacques Bélair durant mes études de maîtrise à l'Université de Montréal.

I am a postdoctoral researcher at École Normale Supérieure de Paris, working in the Applied Math and Computational Biology Lab of David Holcman. I recently completed my PhD at The University of British Columbia under the supervision of Michael J. Ward and Wayne Nagata, with a dissertation on the analysis of patterns in reaction-diffusion equations. I also did a master's degree in Mathematics at the Université de Montréal under the supervision of Jacques Bélair.

Contact: paquin at bio dot ens dot psl dot eu

Resume

Research

My scientific interests lie at the intersection of applied dynamical systems theory and mathematical biology. The overarching theme of my research is the analysis of bifurcations, which characterize the onset of qualitative changes in the overall dynamics resulting from parameters crossing through critical values, in mathematical models of biological systems using combined analytical and numerical approaches. Recently, I have studied the stability of spatio-temporal patterns in certain coupled bulk-surface reaction-diffusion systems, a novel class of models motivated by the compartmentalization of intracellular proteins between membrane-bound and cytosolic species.

Keywords: Dynamical Systems Theory, Asymptotic and Perturbation Methods, Reaction-Diffusion Theory, Mathematical Biology, Scientific Computation and Numerical Continuation Methods.

Publications

  1. Paquin-Lefebvre F, Holcman D. Modeling and asymptotic analysis of the concentration difference in a nanoregion between an influx and outflux diffusion across narrow windows. (2021) arXiv
  2. Paquin-Lefebvre F, Iyaniwura S, Ward MJ. Asymptotics of the Principal Eigenvalue of the Laplacian in 2-D Periodic Domains with Small Traps. Europ. J. Appl. Math. 1-28 (2021). DOI Preprint
  3. Gomez D, Iyaniwura S, Paquin-Lefebvre F, Ward MJ. Pattern Forming Systems Coupling Linear Bulk Diffusion to Dynamically Active Membranes or Cells. To appear in Phil Proc Roy Soc A (2021). Preprint
  4. Kolokolnikov T, Paquin-Lefebvre F, Ward MJ. Competition Instabilities of Pulse Patterns for the 1-D Gierer-Meinhardt and Schnakenberg Models are Subcritical. Nonlinearity. 34(1), 273-312 (2021). DOI Preprint
  5. Kolokolnikov T, Paquin-Lefebvre F, Ward MJ. Stable Asymmetric Spike Equilibria for the Gierer-Meinhardt Model with a Precursor Field. IMA J Appl Math. 85(4), 605-634 (2020). DOI arXiv
  6. Paquin-Lefebvre F, Nagata W, Ward MJ. Weakly Nonlinear Theory for Oscillatory Dynamics in a 1-D PDE-ODE Model of Membrane Dynamics Coupled by a Bulk Diffusion Field. SIAM J Appl Math. 80(3), 1520-1545 (2020). DOI arXiv
  7. Paquin-Lefebvre F, Xu F, DiPietro KL, Lindsay AE, Jilkine A. Pattern Formation in a Coupled Membrane-Bulk Reaction-Diffusion Model for Intracellular Polarization and Oscillations. J Theor Biol. 497, 110242, 23 pages, (2020). DOI arXiv
  8. Paquin-Lefebvre F, Bélair J. On the Effect of Age-Dependent Mortality on the Stability of a System of Delay-Differential Equations Modeling Erythropoiesis. Acta Biotheor. 68, 5-19 (2020). DOI
  9. Paquin-Lefebvre F, Nagata W, Ward MJ. Pattern Formation and Oscillatory Dynamics in a Two-Dimensional Coupled Bulk-Surface Reaction-Diffusion System. SIAM J Appl Dyn Syst. 18(3), 1334-1390 (2019). DOI arXiv PDF

Theses

  1. On the weakly nonlinear analysis of coupled bulk-surface reaction-diffusion systems: theory, numerics and applications. PhD Thesis, UBC, 2020.
  2. Sur un modèle d'érythropoïèse comportant un taux de mortalité dynamique. Mémoire de Maîtrise, UdeM, 2015.

Past Teaching at UBC

2020 WT1: Teaching assistant for MATH406 Variational and Approximate Methods in Applied Mathematics.

2019 WT2: Instructor for MATH101 Integral Calculus with Applications to Physical Sciences and Engineering.