# Symplectic geometry

Lecturer: Guillermo Gallego

Date: 22/02/2017

Time: 17:00

Place: Room 103

Abstract: A symplectic manifold is an even dimensional differentiable manifold in which we define a differential form ω which is closed and non degenerate. Symplectic manifolds have the fundamental structure of phase spaces in hamiltonian dynamics and they constitute the natural way to the formulation of classical mechanics with independence of local coordinates.

The lecturer will do an overview of the three classical formulations of mechanics (Newtonian, Lagrangian and Hamiltonian), giving their geometric meaning. Finally, he will define and explain what a symplectic manifold is and formulate the canonical formalism on it.

## Bibliography

• Vladimir Arnold, Mathematical methods of classical mechanics
• Florian Scheck, Mechanics: from Newton’s laws to deterministic chaos
• Landau, L. D., & Lifshitz, E. M. Classical mechanics