Research group
Graduate students, postdoctoral fellows and undergraduate researchers I have supervised or co-supervised.
Ph.D. students 11
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- Kevin Constantineau — thesis in progress, 2025–present.
- Gabriel Remond-Tiedrez — thesis in progress, 2024–present (co-supervised with Jason Bramburger, Concordia).
- Dominic Blanco, Extensions in Computer-Assisted Analysis for Partial Differential Equations Posed on Unbounded Domains, 2022–2026.
- Miguel Ayala, Computer-assisted proofs for geometry optimization and gap solitons, 2019–2026 (co-supervised with Rustum Choksi, McGill).
- Gabriel Duchesne, Rigorous computer-assisted methods for global structures in dynamical systems, 2019–2025.
- Matthieu Cadiot, Computer-Assisted Analysis for Partial Differential Equations and Nonlocal Equations on Euclidean Spaces, 2020–2025 (co-supervised with J.-C. Nave, McGill).
- Olivier Hénot, Advances in computer-assisted proofs: invariant manifolds and connecting orbits, 2018–2023.
- Maxime Breden, Équations aux dérivées partielles et systèmes dynamiques appliqués à des problèmes issus de la physique et de la biologie, 2014–2017 (co-supervised with Laurent Desvillettes, ENS Cachan).
- Tahmineh Azizi, Neuroscience computationelle et systèmes dynamiques, 2015–2017.
- Andréa Deschênes, Méthode de calcul rigoureux pour les ondes progressives pour les EDP, 2014–2017.
- Pierre-Olivier Vallerand Beaudry, Théorie Computationelle de Morse-Floer, 2011–2013.
Master’s students 13
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- Geoffrey Kelly — thesis in progress, 2026–2028 (co-supervised with Adam Oberman, McGill).
- Marco Mignacca, Rigorous proof of one-dimensional steady-states in a neural field model, 2023–2025.
- Kevin Constantineau, Spatially inhomogeneous two-cycles in ecological integrodifference equations, 2023–2025.
- Matthieu Cadiot, Bifurcations towards periodic solutions in quadratic semilinear partial differential equations, 2018–2020 (co-supervised with Jean-Christophe Nave, McGill).
- Yann Ricaud, Rigorous parameterization of stable and unstable manifolds of fixed points from ODEs with polynomial vector field depending on parameters, 2017–2020.
- Gabriel Duchesne, Computer-assisted proofs of nonlinear Laplace-Beltrami equations on the sphere, 2017–2019.
- Olivier Hénot, Configurations centrales en toile d’araignée, 2017–2018 (co-supervised with Christiane Rousseau, UdeM).
- Francis Desjardins, Construction axiomatique des ensembles de nombres: des naturels aux réels, 2014–2016.
- Maxime Murray, Preuve rigoureuse d'une connection homocline pour l'équation du pont suspendu, 2013–2015.
- Abdoulaye Thiam, A rigorous numerical method for the proof of Galaktionov's conjecture, 2013–2015.
- Andréa Deschênes, Fronts stationnaires pour l'EDP de Swift-Hohenberg via le calcul rigoureux, 2012–2014.
- Maxime Breden, Calcul rigoureux d'un diagramme de bifurcation d'un système d'EDPs (Internship for the Masters I of ENS Cachan, France), May–July 2012.
- Matthieu Vanicat, Calcul rigoureux d'un diagramme de bifurcation d'un système d'EDPs (Internship for the Masters I of ENS Cachan, France), May–July 2012.
Postdoctoral fellows 3
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- Kevin Church, McGill (NSERC Postdoc & CRM-Simons Postdoc), 2019–2022.
- Roberto Castelli, Basque Center for Applied Mathematics (BCAM) (Postdoc), 2010–2011. Title of the project: Rigorous numerics in Floquet theory: computing (un)stable bundles of periodic orbits.
- Gabor Kiss, Basque Center for Applied Mathematics (BCAM) (Postdoc), 2010–2011. Title of the project: Computational fixed-point theory for delay equations with multiple time lags.
International interns 5
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- Joan Gimeno (University of Barcelona). Title of the project: Delay differential equations and celestial mechanics. Fall 2018 and Fall 2019.
- Elena Queirolo (VU University Amsterdam). Title of the project: Rigorous computation of Hopf bifurcations in ODEs. Fall 2016.
- Chris Groothedde (VU University Amsterdam). Title of the project: Rigorous computing of periodic solutions for delay equations. Fall 2014.
- Maxime Breden (ENS Cachan). Title of the project: Calcul rigoureux d'un diagramme de bifurcation d'un système d'EDPs. Spring 2012.
- Matthieu Vanicat (ENS Cachan). Title of the project: Calcul rigoureux d'un diagramme de bifurcation d'un système d'EDPs. Spring 2012.
Undergraduate research students 18
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- Moeez Mohammad (McGill), Energy landscape characterization via computer-assisted proofs and machine learning. SURA Undergraduate Student Research Project, Summer 2023.
- Kevin Constantineau (McGill), Standing 2-cycles in an integrodifference equation model from spatial ecology. SURA Undergraduate Student Research Project, Summer 2022.
- Kevin Constantineau (McGill), Relative equilibria and periodic solutions from platonic solids of vortices on the sphere. NSERC Undergraduate Student Research Project, Summer 2021.
- Kevin Constantineau (McGill), Relative equilibria, bifurcations and periodic orbits in Thomson’s problem via computer-assisted proofs. ISM Undergraduate Scholarships, Summer 2020.
- Clément Fortin (McGill), Gravitational billiards in a vibrating or rotating parabolic domain. Paid Research Assistant, Summer 2020.
- Jordan Paillé (McGill), Computation of two-dimensional manifolds of relative equilibria in the circular restricted four-body problem. Paid Research Assistant, Fall 2019.
- Nathan Maves-Moore (McGill), Computation of two-dimensional manifolds of relative equilibria in the circular restricted four-body problem. Paid Research Assistant, Fall 2019.
- Yvonne Bronsard Alama (McGill), Existence and uniqueness of a periodic solution to a 4th order nonlinear ODE. NSERC Undergraduate Student Research Project, Summer 2018.
- Jordan Paillé (McGill), Computation of two-dimensional manifolds of relative equilibria in the circular restricted four-body problem. SURA Research Award, Summer 2018.
- Nathan Maves-Moore (McGill), Computation of two-dimensional manifolds of relative equilibria in the circular restricted four-body problem. Arts Undergraduate Research Internship Award (ARIA), Summer 2018.
- Yann Ricaud (Laval), Chaos de Shilnikov. FSG Research Summer Scholarships, Summer 2016.
- Yann Ricaud (Laval), Calcul rigoureux de solutions périodiques du problème à quatre corps restreint. ISM-CRM Undergraduate Summer Scholarships, Summer 2015.
- Rosalie Bentz-Moffett (Laval), Solution périodique d'une EDO se ramenant à une solution des équations de Navier-Stokes. NSERC Undergraduate Student Research Project, Summer 2014.
- Julian Ransford (Laval), Calcul rigoureux de solutions périodiques du problème à trois corps restreint. NSERC Undergraduate Student Research Project, Summer 2014.
- Yann Ricaud (Laval), Méthodes numériques rigoureuses pour l'étude des systèmes de Filippov. NSERC Undergraduate Student Research Project, Summer 2014.
- Karine Larouche (Laval), L'étude des systèmes d'EDOs à l'aide du calcul numérique. NSERC Undergraduate Student Research Project, Summer 2013.
- Anaïs Correc (Laval), Calculs de solutions d'une EDP de type gradient. NSERC Undergraduate Student Research Project, Summer 2012.
- Andréa Deschênes (Laval), Calcul rigoureux de connexions hétéroclines d'une EDO. NSERC Undergraduate Student Research Project, Summer 2012.
Undergraduate theses 7
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- Gabriel Duchesne, Les méthodes de preuves assistées par ordinateur pour l'étude des EDO non linéaires, Spring 2017.
- Yann Ricaud, Méthode de continuation et détection de bifurcations, Spring 2016.
- Francis Desjardins, Calcul rigoureux d'une variété stable de l'équation de Fisher-Kolmogorov, Spring 2014.
- Maxime Murray, Théorie du chaos et dynamique symbolique, Spring 2013.
- Anaïs Correc, Calcul d'un diagramme de bifurcations de solutions du BVP de Ginzburg-Landau, Spring 2013.
- Cynthia Paquet, Théorie des bifurcations et calcul pour les solutions stationnaires des EDPs, Spring 2012.
- Andréa Deschênes, Méthodes de calcul des connexions homoclines et hétéroclines des EDOs, Spring 2012.