Mathematics

The PhD program is aimed primarily at graduates in mathematics, physics, engineering, statistics and economics, with quantitative address, and aims to train researchers in the advanced fields of Mathematics. 

It is articulated in 6 curricula

1. Algebra and Geometry
2. Mathematical Analysis
3. Numerical Analysis and Mathematical Modelling
4. Mathematical Physics
5. Probability, Statistics and Mathematical Finance
6. Mathematics in Life Sciences and Physics

The Joint PhD Program in Mathematics promotes research in the following areas:

1. group theory, Lie algebras (MIB); category theory, algebraic geometry (PV), differential geometry (MIB and PV), symplectic (MIB) and hyperbolic (PV) geometry.

2. partial differential equations and their applications; control and optimization theory, nonlinear and functional analysis (MIB and PV); harmonic and geometric analysis (MIB); variational techniques, calculus of variations (PV).

3. study of numerical methods for PDEs with focus on applications; constrained optimization models and methods; computer aided design, approximations of data and functions, numerical linear algebra (MIB and PV).

4. soft matter mathematical modelling, kinetic theory, classical and quantistic field theory, complex systems (PV); fluid mechanics (PV e MIB), integrable systems, Frobenius manifolds, dynamical systems, quantum mechanics (MIB).

5. bayesian statistics, quantum probability, probability measures (PV); statistical mechanics (MIB and PV); random walks, systems,  stochastic equations and control, economical and finantial applications (MIB).

6. studies for biological, biomedical, physical and thermomechanical models (MIB and PV, in collaboration with Surrey University).

Career opportunities

Beyond Academia and public and private research centers, professional opportunities are
- employment in banks and insurance companies to carry out actuarial activities;
- private companies to carry out modeling, data analysis;
- consulting and IT companies;
- statistical and financial consultancy as freelancers;
- teaching, mostly in High Schools.