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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 
Theory
• Symplectic geometry, sub-riemannian geometry

• Geometry of quantum fields and strings

Introduction to topological field theory

Topics:

  1. Localization formulae and equivariant cohomology
  2. Supersymmetric Quantum Mechanics and Morse theory
  3. Supersymmetric sigma-models and topological twist
  4. A and B models, quantum cohomology and mirror symmetry

Representation Theory

  • Finite groups, character theory and irreducible representations.
  • Complex Lie Groups. Solvable and semisimple groups, irreducible finite dimensional representations. Compact forms.
  • Algebraic homogeneous spaces and Borel Weil Bott theorem.
  • Affine group schemes. Hopf algebras. Introduction to quantum groups.

Venue

  • Wednesdays 16:00-18:00: room 134
  • Thursdays 14:00-16:00: March 17 and 24 room 133, March 31 room 137, April room 136

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