SYMPLECTIC MECHANICS

Second cycle degree in MATHEMATICS

Campus: PADOVA

Language: English

Teaching period: First Semester

Lecturer: FRANCO CARDIN

Number of ECTS credits allocated: 6


Syllabus
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 Maslov-H\"ormander.
Hamilton-Jacobi equation, its geometrical solutions and links to the Calculus of
Variations. Conjugate points
theory in calculus of variations.
Relative cohomology and Lusternik-Schnirelman theory. Introduction to Symplectic
Topology: existence and classification of critical points of
functions and applications to generating functions of Lagrangian submanifolds.
The min-max solution of Hamilton-Jacobi equation. Symplectic Topology by Viterbo: towards the solution of the Arnol'd conjecture. Morse theory.