Mathematics

Purpose of the PhD Course

The PhD 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 wide spectrum of topics in modern algebraic and differential geometry and their applications.

Research Topics

• 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 and virtual classes for 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, stochastic geometry, real algebraic geometry
• Geometry of quantum fields and strings
• Complex differential geometry

Seminars

• Algebraic Geometry Seminar
• Complex geometry
• Geometric Structures Seminar
• Geometry and Physics Seminar
• Low dimensional topology
• Mathematical Physics Seminar
• Noncommutative Geometry Seminar

iGAP

Geometers and Physicists collaborate within the iGAP project.

Faculty

Former Faculty Members

Visiting Professors

External Collaborators

Temporary Scientific Staff

PhD Students

Fourth Year Students

Third Year Students

Second Year Students

First Year Students

Previous PhD Theses

Click here to see the previous PhD Theses.

Regulation

Click here to see the regulation of this Ph.D. course (in Italian).