∙ 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

## Mathematical Methods of Quantum Mechanics

## Research topics

We apply geometric, functional-analytic, algebraic, and operator-theoretic methods to the study of models and problems of relevance for quantum mechanics, solid state physics, and theoretical physics.- Many-body quantum dynamics and effective non-linear Schrödinger equations
- Multi-scale methods and emergent effects in quantum systems

## Quantum Groups and Noncommutative Geometry

## Geometry and Mathematical Physics

## Purpose of the PhD Course

The PhD program in Geometry and Mathematical Physics focuses on the study of analytic and geometric aspects of physical phenomena that are of fundamental interest in both pure and applied sciences and covers wide spectrum of topics in modern algebraic and differential geometry and their applications.