报告题目/Title： Invariant theory of Hamiltonian mechanics and related numerical analysis

报 告 人/Speaker： Oscar Cosserat

Affiliation： Göttingen Mathematisches Institut

Time: 20:00-21:00, Aug 19-21, 2025

Zoom Id: 904 645 6677，Password: 2025

会议链接：

//zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456

Abstract: Hamiltonian systems on Poisson manifolds appear naturally in conservative mechanics as a byproduct of Newton's second law. They provide an efficient formalism to handle symmetries and to tackle stability problems. This is why the question of constructing adapted numerical methods is natural. This lecture is devoted to explain properties of Hamiltonian systems and to develop tools in order to construct numerical integrators for such dynamical systems.

We will first define Poisson manifolds and Hamiltonian systems, and explain their properties through numerous examples. We will then introduce the notion of symplectic groupoid, and illustrate the interest and the power of such an approach to study Hamiltonian systems on Poisson manifolds. In particular, we will use symplectic groupoid theory to construct numerical methods that are adapted to Hamiltonian systems. Finally, we will give examples and illustrations in numerical analysis of those constructions.

Lecture 1: Invariant theory of Hamiltonian mechanics and related numerical analysis I, 20:00-21:00, Aug 19, 2025

Lecture 2: Invariant theory of Hamiltonian mechanics and related numerical analysis I II, 20:00-21:00, Aug 20, 2025

Lecture 3: Invariant theory of Hamiltonian mechanics and related numerical analysis I III, 20:00-21:00, Aug 21, 2025

Bio：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.