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 (the subject of my master thesis), 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, starting from 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 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 a physical phenomena as well as merely mathematical tools.
There are many more topics of mathematics that I love. For instance, I am really interested in the formalization of the mathematical aspects for the economic theory and the related models developed in the last century (as the Cobb-Douglas model and the Solow-Swan model). My colleague Mattia Sensi and I have generalized some results concerning the models quoted above, by using classical tools of differential geometry and analysis. More recently, we started to investigate some problems regarding Benford's law from a number-theoretical point of view.
During the 2020 lockdown, I started studying the history and the properties of a very particular set of numbers: the normal numbers. With my colleague Daniele Taufer, we are trying to propose different points of view to face the issues linked with these numbers that still today are mysterious objects.
From 2021 I cooperate with Marco Capolli and Mattia Sensi with the purpose of generalizing the famous Lanchester's model concerning the military strategies during a conflict between two (or more) armies.
In 2021 I started two collaborations in the field of phiolosphy of science and epistemology. The first one regards the role of analogies in mathematical discovery. This project is carried on jointly with Francesco Nappo. Our aim is to provide a novel epistemological account of analogical reasoning in pure mathematics. The second collaboration is a joint work with Michele Loi. We propose a comprehensive account of justice and fairness in the language of probability theory.
Research Summary for AI Ethics Brief #93 (with M. Loi): Group Fairness Is Not Derivable From Justice: a Mathematical Proof (March 11th, 2022).
Article for UNITNMaG: LA MATEMATICA COME MESTIERE - Una ricerca di dottorato sulla meccanica quantistica di Feynman (October 27th, 2017).