Dear students of the Master degree in Mathematics,
the minicourse in
“An introduction to the geometry of integrable Hamiltonian systems”
speaker prof. Daniele Sepe - UFF Niteroi, Brazil, start next Tuesday October 20th.
- Tuesday 20/10/2020, 14:00-16:00,
- Thursday 22/10/2020, 16:00-18:00,
- Thursday 29/10/2020, 15:00-17:00,
- Friday 30/10/2020, 15:00-17:00.
The lessons of the minicourse will be broadcasted streaming via Zoom, recorded and then available. People interested are invited to register to the moodle of the minicourses,
where all the information, materials and zoom links will be available.
To facilitate fast communications and to allow people that has not the univr credentials to attend the minicourse, a telegram group has been created. Please register also there https://t.me/minicourseGHS.
For any information don’t hesitate to contact me (dott. Nicola Sansonetto) organiser of the minicourse.
An important question in Hamiltonian mechanics is to describe qualitative properties of the dynamics under consideration. In general, this is a hard problem but it can be tackled for those systems that are known to be integrable, i.e. that admit the largest number of constants of motion. In spite of their relatively simple dynamical behaviour, integrable Hamiltonian systems play a prominent role in Hamiltonian mechanics and beyond, ranging from symplectic geometry, Lie theory and quantum mechanics. The aim of this course is to provide an introduction to the geometry of such systems from a symplectic perspective. After introducing the necessary tools from symplectic geometry, we will study the structure of integrable Hamiltonian systems near regular points and regular (connected components of) fibres, proving the Darboux-Carathéodory and the Liouville-Arnol'd theorems. The theory will be illustrated by some (simple) examples.