∙ Integrable systems in relation with differential, algebraic and symplectic geometry, as well as with the theory of random matrices, special functions and nonlinear waves, Frobenius manifolds
• Deformation theory, moduli spaces of sheaves and of curves, in relation with supersymmetric gauge theories, strings, Gromov-Witten invariants, orbifolds and automorphisms

• Quantum groups, noncommutative Riemannian and spin geometry, applications to models in mathematical physics

• Mathematical methods of quantum mechanics

• Mathematical aspects of quantum Field Theory and String
Theory

• Symplectic geometry, sub-riemannian geometry

• Geometry of quantum fields and strings

## Introduction to C*-algebras

This course provides a brief introduction to C*-algebras. The course will cover at least the following topics:

- brief recap on Banach spaces and linear operators;

- Banach algebras: spectrum, Gelfand transform, Stone-Weierstrass theorem;

- C*-algebras: definition and basic properties;