Mathematics

  • Duration: 3 years
  • Admission: academic qualifications and interview
  • Coordinator: prof. Massimiliano Mella
  • Head office: agreement with UniFe, Università di Parma (UniPr) and Università di Modena e Reggio-Emilia (UniMoRe)
  • Department: Matematica e informatica
  • Web: homepage of the PhD course
  • Study abroad: at least 1 month
  • Educational purpose: The Ph. D. Program in Mathematics is mainly aimed in training highly qualified professionals, with advanced skills on mathematical models and methods and able to use them also in interdisciplinary applications. They will be ready to work in universities, research institutes, industry, public administration as well as in independent commercial ventures.
    The program is designed to develop an advanced understanding of basic fields of Mathematics and a thorough understanding of one major field of interest.  Emphasis is placed on the abilities of recognizing significant research problems, of formulating solutions, and of transmitting successful outcomes to others.
    The present Doctoral Program is the natural completion of the Courses of Laurea Magistrale in Mathematics, but all the graduates with a scientific-tecnological master degree and with a strong background in Mathematics are well suited to attend the program. On the Doctoral program completion, a successful candidate is expected to be able to independently run research activity leading to relevant and original results.
    The collaboration with domestic and foreign research institutions, including universities and possibly companies, are of relevant importance to accomplish all those objectives, and the Ph.D. students are invited to spend periods of study and research there.
  • Curriculum: no
  • Educational plan: the program of a Ph. D. student in Mathematics consists of structured teaching activities and   research training activites.
    At the beginning of the first year, the  Ph.D. Board  assigns a tutor to each student who guides the student in his\her formative course during the first year, in the choice of the study curriculum as well as in the research training activities. During the first year the tutor,  also considering the possible research interests of the student, helps him\her to take part of the research group. The tutor's task normally ends at the end of the first year, concurrently with the choice of the thesis' supervisor.
    At the end of the three-year course, each Ph.D. student has to  gain 82 credits of structured teaching activities;  these activities will be carried out mainly during the first year and partially during the second year. The research activities (which also aim to the construction of the final thesis) will start the first year, and it will have a predominant role during the third year. The credits related to the structured teaching activities can be gained through the following activities: attendance to transverse teaching activities; specific disciplinary teaching for the Doctorate course  passing the final examination; disciplinary teaching from Master's Degree courses  passing the final examination; attendance to seminaries; internship or a period of study at other Universities, research institutions, external laboratories and industries; attendance to doctoral schools, organized by the student's doctorate course or by other scientific institutions of equal level in Italy or abroad.
    Ph.D. students will be able to carry out tutoring and, after consulting the Ph.D. Board, supplementary teaching activities supporting the teaching of the courses of study; this activity  must not exceed 50 hours per year.
    As far as transverse teaching activities are concerned, during the three-years course students have to gain at least 10 credits through attendance to University courses on language training (English lectures or held in other languages), on the exploitation of research results, on intellectual property and on knowledge of the European and international systems research, also in a management framework.
    With regards to the disciplinary teaching, in accordance with the tutor,  the student may attend courses at the doctoral level and / or master's degree at another Universities. A certificate of participation will be required (together with a declaration which states that the final examination has been passed) in case of courses attended outside the doctoral seats.
    The training  activities also include a research period abroad, although not continuous. . In particular the Ph.D. Student will be allowed to attend a qualified  scientific institution  for a study and\or research period abroad; this period has to range from a minimum of 1 month and a maximum of 18 months.
    At the beginning of each year the student, according to his/her supervisor, proposes his\her annual activity plan to the Ph. D Board. During the first year, this plan has to  take into consideration acquired knowledge and skills , in order to develop the planned research activities.
    In order to promote training in scientific presentation and discussion of the results, attendance to conferences, workshops and schools, suitable for the specific scientific student's profile, will be encouraged; this attendance will be supported by speeches and poster presentations held by the student , on his\her research results.
    As far as the research activities are concerned, the student will take part of one of the research groups, choosing between a wide variety of scientific topics developed by members of Ph. D. Board   at an international level. Group actions: Hopf  Algebras and Quantum Groups, Algebraic Projective Geometry, Geometry and Complex Analysis, Discrete mathematics and Combinatorial geometry, Geometric and algebraic topology of the varieties, Quasi- complex structures, symplectic geometry and CR-structures, History of Mathematics, Partial Differential Equations, Exterior Differential System,Calculus of Variations and applications to Variational problems, Analytic Number Theory, Probability, Continuum Thermomechanics, Kinetic Theory -Gas dynamics, Mathematical models and method for complex systems, Mathematical Methods of Quantum Mechanics, Random Spatial Processes, Mathematical models in Biology, Modeling and Scientific Computing, BEM-FEM coupling, Numerical Optimization and Applications, Numerical methods for Integral Equations, Combinatorial Optimization.
    These topics are supported by the opportunity to acquire knowledge in computer science  and statistics, integrating mathematical knowledge with skills on the high-performance scientific computing (HPC),  logical and technical tools for parallel and distributed computing (grid computing, cloud computing) and models and methods of the Bayesian statistics.
    The tutor and the thesis supervisor (from the 2nd year) have the duty to monitor the formative  course of the student, about attendance to specific courses, national schools for Ph. D. students, specialized seminars, period of study abroad, and the quality of research activities.
    At the end of each year, each student has to write a report on the carried out activities, with a list of his\her work (publications,  speeches, seminars) and has to give a public presentation to the Ph. D. Board  about his\her activity and the results obtained.
    This activity will be evaluated by the Ph. D Board.  Regarding the scientific publications, the Ph. D. Board ,   taking into consideration the tutors’ opinions, will decide if the research has been carried out by the student according to  the scientific objectives of the doctoral program. The  enrollment to the following year of the doctorate is conditioned to the positive  evaluation the Ph. D. Board.
    At the end of the third year of the doctorate, the student has to present a paper and an electronic version of the thesis, together with the list of publications related to his\her research work and other acquired titles. The student has to write the thesis in English;  the thesis will be sent to two external experts in the scientific topic  of the thesis, and they will give a written analytic evaluation. The students are admitted to the final examination only after a positive opinion by the thesis supervisor and if the Ph. D Board , which will give a final score based on the evaluation of the external  experts and on the score of the presentation of the third year. This score, together with the reports of the external  experts, will be sent to the  evaluation committee of the final exam. The students are also allowed to acquire the title of European Doctorate.