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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

Algebraic Methods for Quantum Theories

- introduction to the theory of C*-algebras and von Neumann algebras
- representations
- automorphisms and dynamical systems
- KMS condition
- contraction semigroups
- algebraic formulation of Quantum Mechanics and Statistical Mechanics
- elements on the algebraic and the constructive Quantum Field Theory


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