# Research

The curriculum in Mathematics includes Algebra, Geometry, Mathematical Analysis, Mathematical Logic, and Mathematical Physics. Research within these subject may concern in particular:

- Additive and triangulated Cathegories;
- Representation and Group theory, Lie theory;
- Asymptotic and probabilistic Group theory;
- Calculus of variations, Geometric measure theory, Geometric Analysis, Sub-Riemannian geometry;
- Deterministic and Stochastic Control theory and Differential Games;
- Partial Differential Equations, linear (spectral theory) and nonlinear (motivated either by geometry or by control problems);
- Algebraic and Complex Analysis;
- Celestial Mechanics and KAM theory;
- Hamiltonian systems;
- Algebraic Geometry, arithmetic of elliptic curves and modular forms;
- Number Theory;
- Foundations of Logic.

The curriculum in Computational Mathematics includes Mathematical Finance, Numerical Analysis, Optimization, and Probability. Research within these subject may concern in particular:

- Stochastic methods for Finance;
- Stochastic models in Statistical Physics;
- Integer programming and combinatorial optimization, Nonlinear programming and mixed integer nonlinear programming, methods for large dimensional problems;
- Models for the optimal management of limited resources;
- Methods of numerical approximation for differential and integral equations, extrapolation methods;
- Numerical methods for image processing;
- Numerical linear and nonlinear algebra and applications, numerical software.

For the research activity at the Department of Mathematics see also the Department research pages.

For the research interests of the member of the Faculty Board of the Program see their individual web pages.

For a list of the recent theses of the PhD students click here.