PhD in Geometry and Mathematical Physics

Purpose of the Ph.D. Course

The Ph.D. program in Geometry and Mathematical Physics focuses on the study of analytic and geometric aspects of physical phenomena that are of fundamental interest in both pure and applied sciences and covers a wide spectrum of topics in modern algebraic and differential geometry and their applications.

Research Topics

• Integrable systems in relation to differential, algebraic and symplectic geometry, as well as with the theory of random matrices, special functions and nonlinear waves, Frobenius manifolds
• Deformation theory and virtual classes moduli spaces of sheaves and of curves, in relation to 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

Seminar on Hodge theory

The students of the Geometry and Mathematical Physics sector organize a series of seminars on topics of Hodge Theory.

The most recent placements after Ph.D. at SISSA:

• Mathematical Sciences Research Institute Berkeley - USA,
• Harvard University, Cambridge - USA,
• Mathematical Institute, University of Oxford - UK,
• DAMTP, University of Cambridge - UK,
• Max Planck Institute, Bonn - Germany,
• École Polytechnique, Palaiseau - France