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

Time-reversal invariant topological insulators and a comparison of indices

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Double ramification cycles and integrable hierarchies

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Nakajima varieties

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Stochastic Geometry

Gaussian distributions and invariant metrics, random complex polynomials, random real polynomials, integral geometry and tube formulas, asymptotic methods, distribution of zeroes (univariate case), large deviation principles, random matrices, systems of random equations, Kac-Rice formulas, statistics for geometrical quantities (volume, curvature..), statistics for topological quantities, incidence and enumerative problems, random convex bodies.