Mercoledi' 23 Novembre, ore 15.30, Aula B
Giovedi' 24 Novembre, ore 11, Aula B
Mercoledi' 30 Novembre, ore 15.30, Aula B
Giovedi' 1 Dicembre, ore 11, Aula B
Symplectic geometry is a branch of differential geometry that studies symplectic manifolds,
which are smooth manifolds equipped with closed non-degenerate two-forms. The course
begins with basic concepts such as Hamiltonian vector fields, Poisson brackets, Lagrangian
submanifolds and the Darboux theorem. Examples include cotangent bundles, K ̈ahler man-
ifolds, coadjoint orbits and fibrations of Lagrangian tori. Comparisons will be made with
contact and Poisson manifolds. The second part is about symmetries of symplectic man-
ifolds. Important notions to be introduced are Hamiltonian group actions, moment maps
and their images, and symplectic quotients. Interesting examples are toric manifolds and
moduli space of flat connections on surfaces. The last part of the course is to be on the
applications of symplectic geometry to classical mechanics (Lagrangian and Hamiltonian
mechanics), solving problems on the motion of rigid bodies and integrable systems.
The course is suitable for students who have already taken an introductory course on man-
ifolds (with calculus of di↵erential forms) and who wish to engage their knowledge in a
constructive and useful setting.
Il programma dettagliato del corso è allegato alla sezione "approfondimenti".