Hi there!
My name is Nicolò Cangiotti, and I am a mathematician.
For further information, see my curriculum vitae below.
My research interests sit at the intersection of mathematics and mathematical physics, moving quite freely between probability, stochastic analysis, differential equations, and ideas from differential geometry. A recurring theme in my work is the use of functional integration and infinite-dimensional oscillatory integrals to understand quantum dynamical systems. In this context, I have worked with Sonia Mazzucchi and Sergio Albeverio on the construction of a three-dimensional Feynman path integral for the Schrödinger equation with magnetic field.
Alongside these more theoretical directions, I enjoy working on models inspired by real-world phenomena. With Marco Capolli, Sara Sottile, and Mattia Sensi, I studied systems of ordinary differential equations arising in social and biological modeling, ranging from extensions of Lanchester-type models for military conflicts to compartmental models in epidemiology.
My interests in partial differential equations include coupled field equations such as Klein–Gordon–Maxwell and Schrödinger–Maxwell systems with mixed local and nonlocal interactions, studied in collaboration with Maicol Caponi, Alberto Maione, and Enzo Vitillaro.
More recently, my research has turned to nonlinear Schrödinger equations on periodic metric graphs, where I investigate the existence of ground states and how the geometry of the underlying structure leads to a dimensional crossover between one- and two-dimensional behavior.
Alongside my mathematical work, I am deeply interested in philosophy of science, with a particular focus on the philosophy of mathematics and physics. A central theme of this line of research is the interpretation of Feynman diagrams, which I study both as representations of physical processes and as powerful mathematical tools in their own right.
I am currently involved in two main philosophical projects. Together with Francesco Nappo, I am investigating the role of analogies in mathematical discovery, with the goal of developing a new epistemological account of analogical reasoning in pure mathematics. At the same time, I collaborate with Michele Loi and Marcello di Bello on building a probabilistic framework for thinking about justice and fairness, where tools from probability theory are used to clarify normative concepts.
Earlier in my academic path, I also worked on topics in quantum gravity during my master’s thesis, a subject that still fascinates me and continues to provide a natural bridge between my mathematical and philosophical interests.