Complexity of almost-toric integrable Hamiltonian systems
Event details
| Date | 25.02.2014 |
| Hour | 16:15 › 17:00 |
| Speaker | Christophe Wacheux (EPFL) |
| Location | |
| Category | Conferences - Seminars |
Geometry and Dynamics Seminar
Abstract: In this talk I will discuss integrable Hamiltonian systems on symplectic manifolds. First, I recall the results existing near regular points. Later I will focus on the study of non-degenerate critical points and explain why the transition from them to non-degenrate critical singularities needs a study of their own.
First, the toric systems, that is, integrable Hamiltonian systems whose components of the moment map are periodic. This amounts to the description of elliptic singularities with Atiyah - Guillemin & Sternberg theorem, and Delzant classification by moment polytopes.
Next, the almost-toric systems, that is, integrable Hamiltonian systems whose n-c last components of the moment map are all periodics. We keep the terminology "semi-toric systems" for the case c=1, which is more simple. Study of almost and semi-toric systems is a subject on its own, but today, we shall focus on the almost-toric case.
That is why I will introduce the Williamson indices (k_e,k_f,k_h,k_x) and describe the structure of poset they carry. Lastly, I finish defining the complexity c, and explain its links to all the notions that we have introduced.
Abstract: In this talk I will discuss integrable Hamiltonian systems on symplectic manifolds. First, I recall the results existing near regular points. Later I will focus on the study of non-degenerate critical points and explain why the transition from them to non-degenrate critical singularities needs a study of their own.
First, the toric systems, that is, integrable Hamiltonian systems whose components of the moment map are periodic. This amounts to the description of elliptic singularities with Atiyah - Guillemin & Sternberg theorem, and Delzant classification by moment polytopes.
Next, the almost-toric systems, that is, integrable Hamiltonian systems whose n-c last components of the moment map are all periodics. We keep the terminology "semi-toric systems" for the case c=1, which is more simple. Study of almost and semi-toric systems is a subject on its own, but today, we shall focus on the almost-toric case.
That is why I will introduce the Williamson indices (k_e,k_f,k_h,k_x) and describe the structure of poset they carry. Lastly, I finish defining the complexity c, and explain its links to all the notions that we have introduced.
Practical information
- Expert
- Free
Organizer
- Martins Bruveris