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Geometry and Mathematical Physics

∙ 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 
• 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;


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