Sumários

Lecture 13

21 abril 2020, 09:30 • Leonardo Macarini

Symplectic and Hamiltonian actions. The orbits of the action of the unitary group in the space of Hermitian matrices by conjugation are symplectic manifolds.

Lecture 12

17 abril 2020, 09:30 • Leonardo Macarini

Strictly convex Lagrangians. The Legendre transform is a diffeomorphism for strictly convex Lagrangians with quadratic growth at infinity.

Lecture 11

14 abril 2020, 09:30 • Leonardo Macarini

Lagrangian action. Minimizing properties. The Lagrangian given by the kinetic energy and minimizing geodesics.

Lecture 10

3 abril 2020, 09:30 • Leonardo Macarini

Hamiltonian and symplectic vector fields. Poisson bracket and Poisson algebra. Integrable systems and Arnold-Liouville theorem.

Lecture 9

31 março 2020, 09:30 • Leonardo Macarini

Reeb flows. Symplectization. Contact type hypersurfaces. Examples of hypersurfaces in \R^{2n} that are not of contact type.