The main objective of training highly qualified professionals in the field of Mathematics, with advanced skills in mathematical models and methodologies, which can also be used in interdisciplinary application contexts, is achieved through a series of lectures, seminars, participation in workshops and research periods in third-party institutions which, on the one hand introduce doctoral students to academic and non-academic research and on the other allow them to establish work contacts that will accompany them in the years following graduation. The training is therefore specifically directed towards the ability to recognize significant research problems, to formulate solutions and to transmit the results to others through oral presentations or written work. At the end of the programme, the PhD must be able to: carry out a research activity independently, produce original and relevant results and enter the international scientific community.