Hi there!
My name is Nicolò Cangiotti, and I am a mathematician.
For further information, see my curriculum vitae below.
My research interests span several branches of mathematics, from probability and stochastic analysis to mathematical physics, incorporating concepts from differential geometry. During my Ph.D. studies (2017/2020), I investigated the theory of infinite dimensional oscillatory integrals, focusing on functional integration techniques and applications to quantum dynamical systems. Working with S. Mazzucchi and S. Albeverio, I studied the formulation of a three-dimensional Feynman path integral for the Schrödinger equation with magnetic field.
In 2018, S. Mazzucchi and I defined a renormalization term for the Ogawa integral in the multidimensional case, utilizing R. Ramer's results. In 2022, my mathematical research expanded into several directions.
I collaborated with Marco Capolli, Sara Sottile, and Mattia Sensi on ODE systems, modeling social and biological phenomena. This included generalizing Lanchester's model for military conflict strategies and studying compartmental models in epidemiology.
Additionally, with Maicol Caponi, Alberto Maione, and Enzo Vitillaro, I investigated PDE systems, focusing on Klein-Gordon-Maxwell equations and Schrödinger-Maxwell equations driven by mixed local-nonlocal operators.
More recently, my research has encompassed the study of ground states for the nonlinear Schrödinger equation in periodic metric graphs, particularly investigating the dimensional crossover between one and two dimensions and its impact on the existence of ground states.
Since 2021, my work has extended into philosophy of science, particularly mathematics and physics. A key focus has been the interpretation of Feynman diagrams, examining their dual nature as both physical phenomenon representations and mathematical tools.
I'm currently engaged in two main philosophical collaborations. With Francesco Nappo, I'm exploring the role of analogies in mathematical discovery, aiming to develop a novel epistemological account of analogical reasoning in pure mathematics.
In parallel, I'm working with Michele Loi and Marcello di Bello on developing a comprehensive framework for justice and fairness using probability theory. In the past, I also explored quantum gravity during my master's thesis, a subject that continues to captivate my interest, bridging my mathematical and philosophical research interests.