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Geometry and Mathematical Physics

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 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 
  • Symplectic geometry, sub-riemannian geometry
  • Geometry of quantum fields and strings


Geometers and Physicists collaborate within the iGAP project.


Seminar on Hodge theory

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


PhD Coordinator for Geometry and Mathematical Physics


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.



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

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