The course aims to train students capable of carrying out highly qualified mathematical research, both at universities and other public or private bodies, using mathematical research in any form. The training can occur either in pure mathematics, i.e. fundamental research and with outlets mainly in the academic sphere, or in applied mathematics, with outlets both in applied research in the academic world and in the industrial, financial, commercial, and public domain. The central part of the course consists of the dissertation work, during which the students develop cognitive tools that allow them to deal autonomously, originally, and innovatively with the theoretical and practical problems they will have to face in their future work environments. To provide a solid knowledge base on which to develop these skills, during the initial two years, Ph.D. students attend specialized courses held by internal and external lecturers, usually in English. In addition, Ph.D. students attend seminar series within the department and participate in conferences and workshops in Italy and abroad. Ph.D. students are also encouraged to spend training periods abroad of one or more semesters at centers with which the Ph.D. program has scientific links. This achieves another objective, essential for the modern labor market, to train individuals capable of operating effectively and smoothly in an international environment.
The PhD program is structured as a three-year path that integrates advanced training and original research.
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First Year: Advanced Training. Students follow a personalized study plan, agreed upon with their tutor, selecting specialized courses offered by the doctoral school, including those jointly organized with other Roman universities. Participation in schools and conferences at national and international research institutions is encouraged and supported. The areas covered span the frontiers of mathematics, from algebra and number theory to geometry and analysis, extending to applications in mathematical physics, computational sciences, and modelling.
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Second and Third Year: Intensive Research. The activity focuses on research conducted under the guidance of a supervisor. Active participation in seminars, conferences, and collaborations with other research groups is an integral part of the path.
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Assessment and Defense. Progress is monitored through two annual progress reviews and culminates in the writing and defense of an original thesis. The thesis is evaluated by international referees and defended before an examination board appointed by the Rector.