"Matematica in azione" is a cycle of seminars aimed at gathering young researchers (Master’s and PhD students) working in the field of Applied Maths in an accessible and informal environment.
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The nature of mathematical models
The nature of mathematical models
14:30 13/05/2026 U6-12
14:30 13/05/2026 U6-12
Mathematical modeling acts as a formal bridge between conceptual theory and empirical observation, mapping complex realities—from physics to biomedicine—into a precise geometric language. At its core, it reveals that identifying a model is not just a calculation, but a way to represent the abstract correspondence between our ideas and the physical world through the geometry of estimation.
Prof. Andrea De Gaetano
Director of CNR-IRIB; Distinguished Professor at Óbuda University; Adjunct Professor at Mahidol University
Abstract
Mathematical modeling has become pervasive in applications, not only in physics or economy, but also in biomedicine and other "soft'' sciences. To the conceptual formulation of a model there often follows its identification by statistical parameter estimation, given available observations. While the nature of the modeling process as well as its relationship with the attending statistical computations could both appear obvious to the practitioner, it may be useful to formalize them in a precise way. Insight into the process of (linear and nonlinear) model parameter estimation can be obtained from the description of the geometry of estimation in case space. The objective then is to also describe the geometry of modeling in the abstract, and to show how the correspondence between the conceptual context and the computational context can be formally represented.
Poster 🖼️
Sustainability around the Earth
Sustainability around the Earth
16:45 20/05/2026 U9-09
16:45 20/05/2026 U9-09
Dynamical systems theory provides the mathematical lens to navigate the complex environment of Earth’s orbit, turning natural perturbations into a tool for environmental preservation. At its core, it reveals the existence of "de-orbiting corridors"—natural gravitational highways that allow us to safely dispose of space debris and ensure the long-term sustainability of our cosmic infrastructure.
How dynamical systems theory can help in the design of passive mitigation strategies for the space debris problem
Elisa Maria Alessi
IMATI - CNR
Abstract
Most of the artificial bodies orbiting the Earth are non-functional spacecraft, rocket bodies and fragments. As operational satellites are key assets for life on Earth, the international community is facing the space debris problem by means of different measures, from observations to regulations, from spacecraft design to advanced mathematics. The ultimate goal is to make sustainable the space exploitation. At the moment, one of the most effective mitigation measures is the so-called end-of-life disposal, i.e., the satellite, once the operations are concluded, cannot be left in its orbit, but must be disposed towards an orbit that will not cause any risk to the operational satellites. Natural gravitational and non-gravitational perturbations can be considered to reduce the cost of this maneuver. In this talk, I will introduce the space debris problem and I will focus on the coupled effect of Earth's oblateness and solar radiation pressure. The perturbation in the long term can be written as a series of resonant terms, that produce a variation in the orbit of the satellite. By isolating one term at a time, we can obtain an integrable model. The corresponding phase space can be used to define suitable initial conditions and area-to-mass rati to de-orbit the spacecraft towards the Earth's atmosphere, by increasing naturally the orbital eccentricity. Numerical simulations based on a full dynamical model have confirmed the existence of these trajectories, that have bene called "de-orbiting corridors".
Poster 🖼️
Bayesian Inference for Biodiversity
Bayesian Inference for Biodiversity
16:45 09/06/2026 U9-05
16:45 09/06/2026 U9-05
Statistical inference on biodiversity acts as a powerful mathematical lens that reveals the hidden patterns of life within our most complex ecosystems. At its core, it leverages Bayesian nonparametric methods to map the hierarchical structure of nature, allowing us to estimate the fundamental diversity of our planet—from the smallest fragments to the vast tree flora of the Amazon.
A Bayesian theory for estimation of biodiversity
Prof. Tommaso Rigon
University of Milano-Bicocca
Abstract
Statistical inference on biodiversity has a rich history going back to RA Fisher. An influential ecological theory suggests the existence of a fundamental biodiversity number, denoted alpha, which coincides with the precision parameter of a Dirichlet process. Motivated by this theory, we develop Bayesian nonparametric methods for statistical inference on biodiversity, building on the literature on Gibbs-type priors. We argue that sigma-diversity is the most natural extension of the fundamental biodiversity number and discuss strategies for its estimation. Furthermore, we develop novel theory and methods starting with an Aldous-Pitman process, which serves as the building block for any Gibbs-type prior with a square-root growth rate. We propose a modeling framework that accommodates the hierarchical structure of Linnean taxonomy, offering a more refined approach to quantifying biodiversity. The analysis of a large and comprehensive dataset on Amazon tree flora provides a motivating application.
Conservation laws (01/04/2026)
Conservation laws (01/04/2026)
Conservation laws are mathematical equations that describe how a physical quantity changes over time. At their core, they state a simple but powerful principle: the total amount of a substance in a region changes only by the amount that flows in or out through its boundaries. Today, we explore two fascinating and diverse applications of these laws:
General Non Local Balance Laws: from Clustering to Cryptography
Andrea Salvadori
University of L'Aquila, University of Tours
ARZ-type model of vehicular traffic with local constrained flow
Davide Meroni
University of Milano-Bicocca
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