RESEARCH

PREPRINTS

• Validated integration of semilinear parabolic PDEs. With J.B. van den Berg and R. Sheombarsing. ArXiv:2305.08221. The codes associated to this work can be found here.

PUBLICATIONS

• A posteriori validation of generalized polynomial chaos expansions. SIAM Journal on Applied Dynamical Systems, 22(2): 765-801, 2023. The codes associated to this work can be found here.

• Computer-assisted proof of shear-induced chaos in stochastically perturbed Hopf systems. With M. Engel. The Annals of Applied Probability, 33(2): 1252-1294, 2023. The codes associated to this work can be found here.

• Computer-assisted proofs for some nonlinear diffusion problems. Communications in Nonlinear Science and Numerical Simulation, 109: 106292, 2022. The codes associated to this work can be found here.

• Existence of traveling wave solutions for the Diffusion Poisson Coupled Model: a computer-assisted proof. With C. Chainais-Hillairet and A. Zurek. ESAIM : Mathematical Modelling and Numerical Analysis, 55(4):1669–1697, 2021. The codes associated to this work can be found here.

• On the influence of cross-diffusion in pattern formation. With C. Kuehn and C. Soresina. Journal of Computational Dynamics, 8(2): 213–240, 2021.

• Spontaneous periodic orbits in the Navier-Stokes flow. With J.B. van den Berg, J.-P. Lessard and L. van Veen. Journal of Nonlinear Science, 31(2): 1-64, 2021. The codes associated to this work can be found here.

• Computing invariant sets of random differential equations using polynomial chaos. With C. Kuehn. SIAM Journal on Applied Dynamical Systems, 19(1): 577-618, 2020. The codes associated to this work can be found here.

• Rigorous study of the equilibria of collision kernels appearing in the theory of weak turbulence. With L. Desvillettes. Archive for Rational Mechanics and Analysis, 235 (2): 1151-1176, 2020.

• Rigorous validation of stochastic transition paths. With C. Kuehn. Journal de Mathématiques Pures et Appliquées, 131: 88-129, 2019. The codes associated to this work can be found here.

• Polynomial interpolation and a priori bootstrap for computer-assisted proofs in nonlinear ODEs. With J.-P. Lessard. Discrete and Continuous Dynamical Systems B 23(7): 2825-2858, 2018. The codes associated to this work can be found here.

• Existence and instability of steady states for a triangular cross-diffusion system : a computer-assisted proof. With R. Castelli. Journal of Differential Equations 264(10): 6418-6458, 2018. The codes associated to this work can be found here.

• Applications of improved duality lemmas to the discrete coagulation-fragmentation equations with diffusion.  Kinetic and Related Models 11(2): 279-301, 2018.

• Continuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proof. With J.B. van den Berg, J.-P. Lessard and M. Murray. Journal of Differential Equations 264(5): 3086-3130, 2018. The codes associated to this work can be found here.

• Smoothness of moments of the solutions of discrete coagulation equations with diffusion. With L. Desvillettes and K. Fellner. Monatshefte für Mathematik 183(3): 437-463, 2017.

• Computation of maximal local (un)stable manifold patches by the parameterization method. With J.-P. Lessard and J.D. Mireles James. Indagationes Mathematicae 27(1): 340-367, 2016. The codes associated to this work can be found here.

• Rigorous numerics for nonlinear operators with tridiagonal dominant linear parts. With L. Desvillettes and J.-P. Lessard. Discrete and Continuous Dynamical Systems A 35(10): 4765-4789, 2015. The codes associated to this work can be found here.

• Global bifurcation diagrams of steady states of systems of PDEs via rigorous numerics: a 3-component reaction-diffusion system. With J.-P. Lessard and M. Vanicat. Acta Applicandae Mathematicae 128(1): 113-152, 2013.

POSTER

• MATKIT Workshop "Mathematical Topics in Kinetic Theory". Cambridge, UK, May 2016.

PRESENTATIONS IN CONFERENCES

• Workshop "Parabolic and kinetic models in population dynamics", Institut de Mathématiques de Toulouse, France, September 2022.

• Congrès National d'Analyse Numérique, Minisymposium "Calcul numérique certifié", Evian-les-bains, France, June 2022.

• Workshop "Dynamic, Topology and Computations", Bedlewo, Poland, June 2022.

• Workshop "Asymptotic Behavior of systems of PDE arising in physics and biology : theoretical and numerical points of view", Lille, France, November 2021 .

• ICMS Workshop "Modelling Diffusive Systems : Theory & Biological Applications", online, September 2021 .

• MFO Workshop "Dynamics of Waves and Patterns", Oberwolfach, Germany, August 2021.

• SIAM Conference on Applications of Dynamical Systems, Minisymposium "Computer-Assisted Mathematical Proofs in Nonlinear Dynamics", online, May 2021.

• Equadiff conference, Minisymposium "Computer-assisted proofs in Dynamics", Leiden, Netherlands, July 2019.

• Workshop "Qualitative behaviour of kinetic equations and related problems : numerical and theoretical aspects", Bonn, Germany, June 2019.

• Workshop "Rigorous Computational Dynamics in Infinite Dimensions", Montréal, Canada, April 2019.

• Workshop "Asymptotic Behavior of systems of PDE arising in physics and biology: theoretical and numerical points of view", Lille, France, August 2018.

• Workshop "Dynamic, Topology and Computations", Bedlewo, Poland, June 2018.

• Workshop "Journées Jeunes EDPistes", Nancy, France, March 2018.

• MFO Workshop "Classical and Quantum Mechanical Models of Many-Particle Systems". Oberwolfach, Germany, December 2017.

• Workshop "Recent advances in kinetic equations and applications". Université Paris Dauphine, France, November 2017.

• KI-Net Young Researchers Workshop "Current trends in kinetic theory". College Park, USA, October 2017.

• Workshop "PDEs: Modelling, Analysis and Numerical Simulation". Granada, Spain, June 2017.

• SIAM Conference on Applications of Dynamical Systems, Minisymposium "Dynamical systems techniques in Navier-Stokes flow without material boundaries". Snowbird, USA, May 2017.

• BIRS Workshop "Rigorous Numerics for Infinite Dimensional Nonlinear Dynamics". Banff, Canada, May 2017.

• Lorenz Center Workshop "Computational Proofs for Dynamics in PDEs". Leiden, Netherlands, June 2016.

• Fields Institute Workshop "Extreme events and criticality in fluid mechanics : computations and analysis". Toronto, Canada, January 2016.

• CMS Winter meeting, Session "Computational and Topological Methods in Dynamical Systems". Montréal, Canada, December 2015.

• PIMS Summer School "Rigorous Computing". Vancouver, Canada, June 2015.

• BIRS Workshop "Rigorously Verified Computing for Infinite Dimensional Nonlinear Dynamics". Banff, Canada, September 2014.

• SIAM Annual Meeting, Session "Rigorous Computations for Nonlinear PDEs". Chicago, USA, July 2014.

• BCAM Workshop "Dynamical Systems and Applications". Bilbao, Spain, December 2013.

• CAIMS Annual Meeting, Minisymposium "Rigorous Computations in Dynamical Systems". Québec, Canada, June 2013.

• Workshop "Rigorous Computations for Dynamical Systems". Université Laval, Canada, May 2012.

PRESENTATIONS IN SEMINARS

• Seminar CDSNS, Georgia Tech (online), USA, October 2022.

• Seminar "Dynamical systems - Data-driven modelling of complex systems", Freie Universität Berlin, Germany, July 2022.

• Seminar of the LMAC, Université de Technologie de Compiègne, France, May 2022.

• Seminar  "Équations aux dérivées partielles", Institut de recherche mathématique de Rennes, France, February 2022.

• Seminar  "Modélisation, Analyse et Calcul Scientifique", Institut Camille Jordan, Lyon, France, November 2021.

• Seminar  "Analyse Numérique et Calcul Scientifique", Laboratoire de mathématiques de Besançon (online), France, November 2020.

• Seminar "Computer-assisted mathematical proofs in nonlinear analysis", online, hosted by the CRM, Montreal, August 2020.

• Seminar  "Analyse-probabilité", CEREMADE, Paris, France, February 2020.

• Seminar  "Analyse appliquée", Institut de Mathématiques de Marseille, France, February 2020.

• Seminar of the VALS team, Université Paris-Sud, France, January 2020.

• Seminar of the CMAP, École polytechnique, France, October 2019.

• Seminar series "Coagulation-fragmentation", HIM, Bonn, Germany, June 2019.

• Seminar "Mathématiques pour la Biologie". Institut de Mathématiques de Toulouse, France, February 2019.

• Seminar "Équations aux dérivées partielles". Université de Strasbourg, France, January 2019.

• Seminar "PDE afternoon". Vienna University of Technology, Austria, January 2019.

• Seminar "Modélisation, Analyse & Simulation". Université Paris Descartes, France, December 2018.

• Seminar of the SERENA team. Inria, Paris, December 2018.

• Seminar "Dynamics & Numerics". Technical University of Munich, Germany, November 2018.

• Seminar. Université de Haute-Alsace, Mulhouse, France, February 2018.

• Seminar "Oberseminar Dynamics". Technical University of Munich, Germany, November 2017.

• Seminar "Applied Mathematics". McGill University, Canada, October 2017.

• Seminar "Applied and Computational Analysis", University of Cambridge, UK, June 2017.

• Seminar "Geometric Analysis and Partial Differential Equations". University of Cambridge, UK, June 2017.