Matias Delgadino
Mathematics
From an early age, Argentinian Matias Delgadino wanted to understand the world, and the tool he chose to do so was applied mathematics. Today he is a mathematician who tracks down patterns. With a degree in mathematics from the National University of Córdoba in Argentina, he went on to earn his doctorate at the University of Maryland in the United States. He carried out two post-doctoral internships: the first at the International Center for Theoretical Physics, in Italy, and the last at Imperial College, UK. His research deals with self-organization, a process in which ordered patterns emerge from disordered systems. This work has great potential for applications in machine learning. Previously an adjunct professor at the Pontifical Catholic University of Rio de Janeiro, he is currently a researcher at the University of Texas, USA.
Delgadino has always been fascinated by the patterns we can find in everyday life, such as raindrops falling on a car window or the fractal shape of broccoli or cauliflower. After so many years of study, he discovered that science has many answers, but the most interesting thing is always what we cannot yet explain.
Projects
Ever pondered why ducks fly in a V-formation or why fish school together? These are instances of self-organization, a process where a system initially in disarray evolves into an ordered pattern through the individual interactions of its constituent agents, without any central coordination.
Typically, such behavior emerges when the system comprises a large number of agents, and the system’s local fluctuations can be overlooked in favor of macroscopic dynamics. As the number of agents approaches infinity, this limit can be expressed using a non-linear Partial Differential Equation (PDE), often referred to as the mean-field limit.
This project aims to quantitatively understand when the mean-field limit serves as an accurate descriptor of the system and the microscopic system’s fluctuations around this limit. We hope to apply this theory to characterize the convergence of certain machine learning algorithms quantitatively.
