**Title of the course:** Symplectic geometry and dynamics on group manifolds

**Instructor:** Prof. George Jorjadze

**Institution:** Free University of Tbilisi, Razmadze Mathematical Institute of TSU

**Dates:** 18-26 September 2017

**Prerequisites:** Classical and quantum mechanics, field theory, elements of group theory

**Level:** Graduate, advanced undergraduate

**Abstract:**

Lecture 1. Review of Lagrangian and Hamiltonian dynamics;

First Noether theorem;

Gauge invariant systems and second Noether theorem;

Faddeev-Jackiw method.

Lecture 2. Elements of differential geometry;

Generalized Hamiltonian dynamics;

Symplectic manifolds;

Symplectic structure on the space of solutions.

Lecture 3. Lie algebras, Killing form;

Exponential map and Lie groups;

Group manifolds, vector fields and 1-forms;

Moment map, co-cycles of Lie algebras.

Lecture 4. Liouville model;

Free particle in a curved space;

Particle dynamics on a group manifold;

Particle dynamics on AdS and dS spaces.

Lecture 5. Free field theory on a cylinder;

Chiral symplectic forms;

WZW theory;

Coset WZW models.

Lecture 6. Solution of exercises and problems.

**Language:** EN