It may well be doubted whether, in all the range of Science, there is any field so fascinating to the explorer - so rich in hidden treasures - so fruitful in delightful surprises - as that of Pure MathematicsLewis Carroll

Hi there!

Since June 2021, I am a PostDoc at the Department of Mathematics of the Polytechnic University of Milan. I am part of the group of prof. Giovanni Valente.

For further information, see my curriculum vitae below.

Research Interests

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.

Research Hobbies

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.

Philosophical Research

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.

Thesis

  • 2020 - Ph.D. Thesis: Feynman path integral for Schrödinger equation with magnetic field
    (see Download page and SLIDES)
    Supevisor: Sonia Mazzucchi.

  • 2016 - Master Thesis: A Discrete Approach to Quantum Gravity
    (see
    Download page and SLIDES)
    Advisor: Vittorino Talamini. Co-advisors: Stefano Ansoldi and Sebastiano Sonego.

  • 2012 - Bachelor Thesis: Mathematical Aspects of the Special Theory of Relativity
    (see Download page)
    Advisor: Stefano Ansoldi.