∙ 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

## Topology change and selection rules for high-dimensional spin(1,n)0-Lorentzian cobordisms

## Mathematical Methods of Condensed Matter Physics

Topics to be covered include:

-) Introduction to lattice Schroedinger operators.

-) Disordered systems. Anderson localization, supersymmetric mapping.

-) Topological transport, bulk-edge duality.

-) Many-body systems, renormalization group.

Lecture period: May 18 - June 26. Duration: 30 hours.

References: