The Ph.D. program in Mathematics lasts 3 years and aims to train its students for a professional or academic career, in the area of Pure and Applied Mathematics. To attain this goal, the doctoral program provides: - a broad and high-level preparation in mathematics; - the opportunity to deepen mathematical understanding and abilities through scientific research; - participation in a research program in promising areas of mathematics or its applications in an interdisciplinary setting. The excellence of the research performed in the Department together with the wide-ranging collaborative relationships maintained by researchers in the Department of Mathematics guarantee the high quality of the doctoral program. Our doctoral program belongs to the Vito Volterra Doctoral School, which is an additional opportunity for enriching the scientific and cultural value of our program. The doctoral program starts every year at the beginning of November and, for the following three years the students attend courses, develop an individual research project under the guidance of a supervisor, and participate to the research activities of the Department of Mathematics.