The PhD Program in Mathematics prepares students for professional or academic careers in the field of mathematics and its applications. To achieve this goal, the program provides: - a high-level and broad-based mathematical education; - the opportunity to develop and refine skills for conducting scientific research; - participation in research groups engaged in the most current and promising areas of mathematics and its applications. The quality of the program's advanced education is ensured by the excellence of the Department of Mathematics' research activities (ranked among the best in Italy according to the VQR evaluation) and by the extensive network of scientific collaborations maintained by the Department’s researchers. The PhD Program’s affiliation with the Vito Volterra Doctoral School further enhances its educational opportunities as well as its scientific and cultural value. The program trains young researchers in both pure and applied mathematics. Studies in pure mathematics are intended for doctoral candidates who wish to explore the various aspects of mathematics in depth. The Department offers a wide range of research topics, from the most abstract areas to those directly inspired by the natural sciences. Studies in applied mathematics are aimed at candidates with a strong intellectual curiosity for scientific, technological, economic, and social problems that can be addressed using mathematical methods. These studies provide an opportunity to broaden one’s knowledge base and to appreciate—and contribute to—the role of mathematics in real-world applications. The PhD program spans three years. During the first year, students attend courses to complete their training and begin participating in the Department’s research activities. At the end of the first year, candidates must pass a qualifying exam through which the Academic Board evaluates their acquisition of the knowledge and skills necessary to undertake the thesis work. The second year is devoted to scientific development and to preparing the dissertation, which will be finalized in the third year. The results of the thesis work are presented to the Department in a dedicated seminar session and subsequently discussed by the candidates during the final examination. Further information is available on https://phd.uniroma1.it/web/MATHEMATICS_nD3519_EN.aspx