The PhD curriculum in "Mathematics" includes a variety of scientific topics ranging from Logic, Geometry, to Mathematical Analysis, Numerical Analysis and Operational Research. PhD students in Mathematics are usually affiliated with the Mathematics Division. Moreover, the PhD programs in Physics include activities at the frontier of different scientific disciplines in connection to other Science Divisions including Physics, Earth Sciences, and Computer Science.
The activities carried out within the Mathematical Division can be divided into two main fields, sometimes interconnected each other, both mixing theoretical and computational-experimental aspects.
The first area concerns mathematical methods for the study of information and shape. The basic ideas of information and shape are detailed in a plurality of points of view: dynamic systems and morphogenesis, knot theory and topology, differential geometry, algebraic fields – with applications in biology, art, design, common life. Therefore, the main targets in this area are given by (a) application of the theory of dynamical systems to the study of morphogenetic fields; (b) topology and knot theory with applications to computational design and aesthetics; (c) analysis of geometric structures and physical properties with high degree of symmetry; (d) study of rings of integers in number fields, classification of their modules, connected with computability; (e) methods of model theory for modules on rings (f) study of differential equations and functions of several complex variables with applications in geometry.
The second area is related to mathematical methods for industrial and finance applications. Theoretical and numerical models are developed for the study of issues related to various topics of interest for enterprises and finance operators. In particular this line of research is focused on the following targets: (a) analysis and control of linear and nonlinear dynamic systems (also under fault conditions), of robotic systems, power systems and energy conversion; (b) study of impact problems through modeling, numerical simulation and analysis of experimental results; (c) optimization problems, classification and regression in logistics, finance, electricity market, in biology; (d) analysis and image reconstruction by numerical techniques; (e) numerical evidence of blow-up for the Navier-Stokes equations; (f) resolution of differential equations through numerical methods in finance.
The PhD program in Mathematics includes a period which may vary from three to six months, to be spent into a foreign institution connected with the carried out research project.
Moreover, several PhD students in Physics are also being included in the applied research Program EUREKA, financed in collaboration with Regione Marche, Unicam and enterprises of Marche Region. Those projects may involve different topics of interest for local enterprises, ranging from sustainable energy development to prototype design and modeling, optical systems, and more.