[cangiotti]

Postdoc, Politecnico di Milano

**Email:** *nicolo.cangiotti AT polimi.it*

My research interests are various: from the branch of probability and stochastic analysis to mathematical physics, also using several concepts of differential geometry. In the past I have also approached the world of quantum gravity which still fascinates me. During my Ph.D. studies (2017/2020), I have investigated the theory of infinite dimensional oscillatory integrals. In particular, I was involved in the study of functional integration techniques and applications to quantum dynamical systems. More specifically, I worked with S. Mazzucchi and S. Albeverio on the formulation of a three-dimensional Feynman path integral for the Schrödinger equation with magnetic field by means infinite dimensional oscillatory integrals. Furthermore, in 2018 S. Mazzucchi and I defined a renormalization term for the Ogawa integral in the multidimensional case, by using a result due by R. Ramer. In 2020, I started a research around the Schauder and Sobolev estimates in the theory of parabolic equations (joint work with Lorenzo Marino), with the aim of generalizing a result obtained by N. V. Krylov and E. Priola. From 2021, my research has moved also in the field of philosophy of science (especially mathematics and physics, see also below). My main focus regards the interpretation of Feynman diagrams that could be considered as depiction representing physical phenomena as well as merely mathematical tools. On the side of mathematics, in 2022 I began working on several topics in mathematical analysis. On the one hand, I have investigated some ODE systems (with with Marco Capolli, Sara Sottile, and Mattia Sensi) for modeling social and biological phenomena (fromt the generaliziatio of the famous Lanchester's model, concerning the military strategies during a conflict between twom, or more, armies to the survey of compartmental models in epidemiology). On the other hand, my resarch has moved also in the field of PDE systems, by considering both Klein-Gordon-Maxwell equations and Schrödinger-Maxwell equations driven by mixed local-nonlocal operators (this is a jont project with Maicol Caponi, Alberto Maione, and Enzo Vitillaro).

**Home-page:** https://www.nicolocangiotti.eu/

**arxiv id:** cangiotti_n_1

**orcid id:** 0000-0003-2200-446X

- N. Cangiotti - M. Caponi - A. Maione - E. Vitillaro (
*Fractional Calculus and Applied Analysis*)

Schrödinger-Maxwell equations driven by mixed local-nonlocal operators (2024) - N. Cangiotti - M. Caponi - A. Maione - E. Vitillaro (
*Milan Journal of Mathematics*)

Klein-Gordon-Maxwell equations driven by mixed local-nonlocal operators (2023) - N. Cangiotti - M. Capolli (preprint)

Morrey-Campanato Functional Spaces for Carnot Groups (2023) - N. Cangiotti - M. Capolli - M. Sensi (
*Operational Research*)

A generalization of unaimed fire Lanchester’s model in multi-battle warfare (2023) - N. Cangiotti - M. Capolli - M. Sensi - S. Sottile (
*Bollettino dell'Unione Matematica Italiana*)

A survey on Lyapunov functions for epidemic compartmental models (2023) - N. Cangiotti - M. Sensi (
*Indian Journal of Pure and Applied Mathematics*)

Exact solutions for a Solow-Swan model with non-constant returns to scale (2023) - S. Albeverio - N. Cangiotti - S. Mazzucchi (
*Communications in Mathematical Physics*)

A rigorous mathematical construction of Feynman path integrals for the Schrödinger equation with magnetic field (2020)