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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

Topics in advanced algebra

An introduction to the theory of derived functors in homological algebra, and its applications to sheaves and other geometric and algebraic objects.
  • Basic notions: categories, functors, abelian categories, complexes
  • Derived functors: injective objects, right derived functors, long exact sequence of a derived functor, acyclic resolutions, delta-functors.
  • Introduction to sheaves: presheaves, sheaves, étalé space, direct and inverse images

Advanced Geometry 2

Smooth manifolds and differential topology

Rooms:
Lectures from 26/09 to 24/10 are in room 005
Lectures from 26/10 to 19/12 are in room 133

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