The main research topics are listed below:

• Artificial Intelligence, Knowledge Representation and Reasoning, Answer Set Programming, Logic Programming, Constraint Satisfaction Problems.
• Artificial Intelligence in multidisciplinary contexts
• Databases, Data and Knowledge Integration, Data and Text-Mining, Knowledge Management.
• Theoretical Computer Science, Game theory, Decidability and Complexity Theory.
• Grid Computing, Computational Science, Cellular Automata.
• Optimization Models and Methods for solving problems in Transport and Logistics.
• Nonlinear optimization and Machine Learning
• Combinatorics.
• Study of canonical models of surfaces of general type. Algebraic curves and their moduli spaces. Groups and Graphs.
• Interactions between algebra and geometry and between geometry and mathematical physics in modern and contemporary Mathematics. Historical developments of the decisions theory. History of the mathematics in the didactical field. Mathematic teaching with particular interest in the role and in the use of the technology.
• Calculus of variations. Variational methods in Nonlinear Analysis. Critical point Theory and applications to nonlinear PDE. Geometry of Banach spaces. Local and nonlocal ODE. Approximation methods. Minimum problems and projections. Equilibrium problems. Uniform distribution and discrepancy. Monte Carlo type integration methods.
• Random fields, namely: percolation, statistical mechanics, interacting particle systems, dynamic systems, quantitative finance, stochastic simulation and mathematical statistics.
• Quantum Theory problems. Group-theoretic approach to the interaction theory. Semiclassical models for the electricity and heat transmission in semiconductors. Coupling problems in devices-electrical networks.
• Sequences of Sheffer polynomials and approximation of the involved operators. Numerical approximation of solutions to high order partial differential equations under boundary conditions or initial data. Approximations for Scattered Data and rational interpolation. Applications to engineering problems and statistics.

Courses are held in the University by members of the scientific board and by national and international experts and Professors, highly qualified in the disciplines of the scientific areas included in the program. Courses may take the form of standard-type courses, seminars, and project-based courses, each of one will be associated with a corresponding number of credits. 

Students must achieve a minimim of 24 credits over 3 years, divided into a minimum of 18 credits from specialized courses, and at least 6 credits of cross-curricular courses available in University Catalogue. All of these courses require mandatory attendance and a final assessment by which corresponding credits are awarded.

Students must submit a study plan, which may be revised periodically (approximately every three months), in order to assess it to possible changes in the course list, or to specific needs due to the advancement of their PhD career.

Visit the course page for additional information and the current course schedule.

Seminars are an integral part of the training activities available to doctoral students. The University, the member of the scientific board, but also national and international experts and Professors, offer specialized seminars in their field of study, including laboratory activities.

An updated list of seminars is available here.

The research training activities of the PhD in Mathematics and Computer Science include experiences and tools that help the doctoral student to reach the following objectives:
-Acquisition of specialist knowledge: thanks to the advanced courses and seminars provided as part of the doctoral course, the doctoral student explores specific topics of mathematics and computer science, thereby developing a robust theoretical and methodological foundation.
- Development of practical skills: The doctoral student is instructed in the use of computational tools, programming languages and specialized software for  conducting experiments, analyzing data and developing models.
- Development of research projects: The doctoral student works under the supervision of a tutor, learning to formulate hypotheses, design experiments, collect and analyse data, and finally to present and publish the results obtained.
- Engagement with the scientific community: Attendance of national and international conferences, workshops and seminars provides doctoral students with the opportunity to get in touch with other researchers, gain valuable insights to the state of the art in their research fields and establish durable and profitable scientific collaborations. Furthermore, the mandatory abroad research period will facilitate their international scientific networking. 
 

In addition to the acquisition of technical skills, doctoral students have the opportunity to develop a range of soft skills, including research dissemination, teamwork, time management, and independency in facing research challenges. The PhD course facilitates involvement in third mission activities, which contribute to the development of these skills.

At the beginning of their doctoral program each doctoral student, in consultation with their supervisors defines the research project that will be developed during the three years that will culminate in the writing of the thesis. The supervisors will assist the doctoral student in defining the steps and partial objectives to be achieved, while the college will monitor and verify the achievement of the planned goals.

It is planned at least one confrontation per year of the doctoral students with high-profile researchers with expertise in the research topics covered by the training project. This confrontation will take place during end-of-year examination, with heterogeneous board of members from inside and outside the university.

The PhD program in Mathematics and Computer Science aims to train highly qualified researchers and professionals in the fields of mathematics and computer science.

The versatility of the course trains professionals with their own autonomy and critical capacity, skills that enable them to emerge in the world of work, both in scientific research and in entrepreneurship and business creation.

The training paths are aimed at a quick entry into the world of work, which today is increasingly looking for professionals with training that combines the specialized skills typical of computer science with solid mathematical foundations.

The various possibilities offered to our students include an academic career as a researcher or lecturer in Italy or abroad or highly specialized research activity in public and private companies in the fields of artificial intelligence, big data analytics, natural language processing, knowledge management, optimization and logistics. Finally, future Ph.D.s will have gained the skills to pursue teaching careers in secondary schools as well.