Sébastien Bertrand, PhD

Current position:

Postdoctoral fellow (01/2018 to present) at the Department of Physics,
Faculty of Nuclear Sciences and Physical Engineering,
Czech Technical University in Prague.
Currently funded by a postdoctoral fellowship provided by the NSERC.

Contact info:

Email: bertrseb@fjfi.cvut.cz
Office: #443, Břehová 78/7, 115 19 Praha 1, Prague, Czech Republic.

Researcher biography:

After completing my PhD in applied mathematics at the University of Montreal in 2017, I continued my scientific career under the supervision of Libor Šnobl at the Czech Technical University in Prague thanks to a two-year postdoctoral fellowship provided by the FRQNT (2018-2019). I have been awarded another two-year postdoctoral fellowship from NSERC of Canada to continue my research projects (2020-2021). My two current research projects focus on:

  1. Superintegrable Hamiltonian systems admitting non-zero magnetic fields

    Two well-known examples of superintegrable systems are the harmonic oscillator and the Kepler(-Coulomb) problem. Superintegrable systems possess a high number of conservation laws, which leads to remarkable physical and mathematical properties. In some cases, (super)integrability and separebility are closely related, e.g. in magneticless natural Hamiltonians systems with quadratic integrals of motion or in the context of general relativity and black-hole geodesic. This project focuses on classical and quantum Hamiltonian systems admitting nonzero magnetic fields. Physical applications of these results might be used e.g. for plasma confinement.
    Collaborators: Libor Šnobl, Antonella Marchesiello
     
  2. Supersymmetric integrable models and their differential geometry

    The main objective of this project is to investigate supersymmetric (soliton) integrable models via differential geometry and Lie symmetry approaches. In the past, we constructed the structural equations for the supersymmetric immersions of surfaces and supermanifolds in superspaces with a constant prescribed curvature, i.e. Euclidean, spherical and hyperbolic superspaces. We also constructed supersymmetric versions of the Fokas-Gel'fand formula for the immersion of solitonic supermanifolds in Lie superalgebra. In the future, integrability properties, such as the construction of new Lax pairs, Bäcklund and Darboux transformations, are to be studied in this project.
    Collaborators: A. Michel Grundland, Alexander J. Hariton

Topics of research:

  • Superintegrable Hamiltonian systems;
  • Conservation laws in discrete physics;
  • Soliton integrable models;
  • Differential geometry of supersymmetric systems;
  • Symmetries of differential equations;
  • Lie groups and Lie algebras.