Theses and work opportunities

Come to the dark side. We have cookies!

You can work on theses not only with me, but in general with the Numerical Linear Algebra working group at the University of Pisa. The group is currently split between the Mathematics (Bini, Meini, Steffé) and Computer Science departments (Bevilacqua, Del Corso, Gemignani, Menchi, Poloni, Romani).

There is also a research group in Numerical Analysis coming from the previous Department of Applied Mathematics: Aceto, Ghelardoni, Magherini.

General research topics

There are research seminars in numerical analysis and linear algebra — check them out if you are in Pisa, it's a great way to get to know what we do and what's going on research-wise.

• Matrix equations: algebraic Riccati equations, quadratic and other nonlinear matrix equations, with applications to control theory, probability and econometrics. (Bini, Meini, Poloni)
• Structured matrices: Toeplitz, semiseparable, Cauchy-like, other matrix algebras. Fast algorithms and theoretical aspects. (Bevilacqua, Bini, Del Corso, Gemignani, Romani)
• Numerical methods for polynomial root-finding: Ehrlich-Aberth iteration, eigensolvers, choice of initial values and inclusion sets for the roots (Bini, Gemignani)
• Matrix means: theoretical and computational aspects of means on matrix manifolds (Bini, Meini, Poloni)
• Numerical methods for ordinary differential equations: boundary value methods and block boundary value methods, eigenvalues of Sturm-Liouville problems (Aceto, Ghelardoni, Magherini).

If you have no idea what all these words mean, you can ask us or take a look at our research pages. Look for conference talks, they are often the clearer expositions.

More specific thesis or work proposals vary depending on the moment and are available on request.

Requirements and work structure

All projects will require some mathematics/linear algebra work (proving theorems and bounds, understanding why the algorithms work) and some programming (coding/testing the algorithms). The division between the two varies greatly according to the project: some are very programming-intensive, some are more theoretical and the programming is limited to quick testing with Matlab

You should be (at least somehow) familiar with linear algebra and matrix theory and some programming language (Matlab most frequently, but also Python, C, Fortran...) and willing to work at least a little bit with both these tools. Clearly the required competence level varies according to the specific project: a bachelor's thesis is not the same thing as a PhD project.

Your background can be in Mathematics (pure or applied), Computer Science or even some branches of Engineering.

Why should I choose your group?

• Because you enjoy both mathematics and programming, at least to some extent, and like elegant but practical algorithms.
• Good work opportunities: mathematicians with a programming background are a very good hire in many branches of industry. Matlab, which is our main working tool, is very used in the engineering industry and Matlab skills are often a premium.
• Good opportunities for staying in the Academia: as it is a more "practical" subfield of mathematics, there are more open positions in numerical analysis, in Europe and worldwide, than in most other fields of mathematics.
• Pleasant environment and working group. Research collaborations with several groups in Europe.
• Get to research soon: although some of the older tricks date back to Gauss, numerical linear algebra is a relatively young field. As such, catching up with the state of the art does not take an incredibly long time, and you will be able to do research work starting early in your graduate career.
• Friendly and multicultural international community: people in our field are generally open and friendly; they will not look down on new students at international conferences. At congresses, you will meet people with different academical backgrounds: mathematicians, computer scientists, sometimes engineers. The community benefits greatly of this interchange of cultures.

Funding opportunities

• PhD positions: typically, PhD positions in Italy are not managed directly by the workgroup, but are assigned and funded via common admission tests at the department level. Both the Mathematics and Computer Science department of the University of Pisa offer paid Ph.D. positions, as well as the Scuola Normale (corsi di perfezionamento), another well-known institute in Pisa. Both have additional positions for students from outside the European Community. Deadlines are in Spring and Autumn.
• Humboldt grants: as an additional opportunity, if you come from Germany, you can apply for postdoctoral grants of the Humboldt Foundation. F. Poloni is a former Humboldt fellow and as such can be the academic host for a prospective German Humboldt Fellow coming to Italy.
• Other funding opportunities may be available through financed research projects. Contact F. Poloni or other people in the workgroup.