
SYMPLECTIC MECHANICS
Second cycle degree in MATHEMATICS
Campus:
PADOVA
Language:
English
Teaching period:
First Semester
Lecturer:
FRANCO CARDIN
Number of ECTS credits allocated:
6
Prerequisites:

Elementary Calculus and Geometry 
Examination methods:

Written. 
Course unit contents:

Essential of Differential Geometry and Exterior Differential Calculus.
Cohomology.
Riemannian manifolds:
Existence of metrics, Whitney theorem.
Symplectic Geometry:
Symplectic manifolds.
Introduction and developments of Hamiltonian Mechanics on symplectic manifolds.
Local and global parameterization of the Lagrangian submanifolds and their
generating functions. Theorem
of MaslovH\"ormander.
HamiltonJacobi equation, its geometrical solutions and links to the Calculus of
Variations. Conjugate points
theory in calculus of variations.
Relative cohomology and LusternikSchnirelman theory. Introduction to Symplectic
Topology: existence and classification of critical points of
functions and applications to generating functions of Lagrangian submanifolds.
The minmax solution of HamiltonJacobi equation. Symplectic Topology by Viterbo: towards the solution of the Arnol'd conjecture. Morse theory. 

