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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

Moduli spaces of Riemann surfaces

Please notice that if on Tuesday 14 there is already an Algebraic Geometry seminar scheduled, the corresponding lecture is postponed to Friday 17, 11:00-13:00

Self-adjoint operators in Mathematical Physics

venue and schedule: room A-136, Monday 11-13, Tuesday 11-13
start: Monday 9 February 2015
end: Tuesday 14 April 2015

Synopsis:

Geometric Control Theory

PART 1: Controllability
-) Control systems: accessibility, controllability
-) Controllability of linear systems
-) Families of vector fields. Lie algebras
-) The Frobenious theorem
-) The orbit Theorem and the Krener theorem
-) Symmetric families: the Chow theorem
-) Compatible vector fields
-) Recurrent drift
-) Systems with unbounded controls

PART 2: Optimal control
-) Existence. The Filippov theorem
-) First order conditions. The Pontryagin Maximum Principle
-) Synthesis theory

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