Speaker: Oscar Cosserat
Göttingen Mathematisches Institut
This course explores the fascinating interplay between Poisson geometry, Hamiltonian mechanics, and numerical integration methods. We will develop tools to construct numerical integrators for Hamiltonian dynamical systems on Poisson manifolds.
Part 1 of the series
Wednesday, September 17, 2025
05:00 PM IST
Abstract: We define Poisson manifolds and review the notions we need for this lecture : Hamiltonian vector fields, first integrals, Casimir functions, symplectic foliation... The end of this first lecture is devoted to explain why traditional numerical tools do not straightforwardly apply to Hamiltonian systems on Poisson manifolds.
This talk has ended — see the recording.
Part 2 of the series
Wednesday, September 24, 2025
05:00 PM IST
Abstract: We start by defining groupoids and relate them to Poisson manifolds through the concept of symplectic groupoid. Geometrical tools such as Lagrangian bisections will be defined and explained. In the last part of this session, we introduce so-called "bi-realisations". Those are local forms of symplectic groupoids. On bi-realisations, we will explain how a Hamilton-Jacobi allows to approximate Hamiltonian dynamics on Poisson manifolds.
This talk has ended — see the recording.
Part 3 of the series
Wednesday, October 1, 2025
05:00 PM IST
Abstract: To finish, we will introduce pre-Lie algebras to solve Hamilton-Jacobi equation at arbitrary order and obtain Poisson integrators discretising Hamiltonian dynamics in that way. Geometric properties will be gathered and explained. This last session contains numerical simulations on concrete examples such as Lotka-Volterra systems and rigid body dynamics. To conclude, we will summarize the results of this geometric approach to numerical analysis and give several perspectives.
This talk has ended — see the recording.
Göttingen Mathematisches Institut
Oscar Cosserat is a postdoctoral researcher at the Göttingen Mathematisches Institut, in Germany. He received his PhD in 2023 from the University of La Rochelle, France. His research focuses on the interplay between theoretical mechanics, numerical analysis and differential geometry.