Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 20-01-2025 al 26-01-2025
Lunedì 20 gennaio 2025
Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Winter School on Variational and PDE's Methods in Geometric Analysis
Program:
- 9:30 Rivière (Minicourse Part I)
- 11:30 Lamy (Selected talk)
- 14:00 Pigati (Minicourse Part I)
- 16:00 Cabezas-Rivas (Selected talk)
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
Martedì 21 gennaio 2025
Ore 14:30, aula d'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Francesca Carocci (Università di Roma Tor Vergata)
A logarithmic approach to linear series
Maps to projective space are given by basepoint-free linear series, thus these are key to understanding the extrinsic geometry of algebraic curves. How does a linear series degenerate when the underlying curve degenerates and becomes nodal? Eisenbud and Harris gave a satisfactory answer to this question when the nodal curve is of compact type. I will report on a joint work in progress with Luca Battistella and Jonathan Wise, in which we review this question from a moduli-theoretic and logarithmic perspective. The logarithmic prospective helps understanding the rich polyhedral and combinatorial structures underlying degenerations of linear series; these are linked with the theory of matroids and Bruhat–Tits buildings.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Martedì 21 gennaio 2025
Ore 15:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
Marcel Guardia (Universitat de Barcelona)
Diffusive behavior along mean motion resonances in the 3 body problem
Consider the Restricted Planar Elliptic Three Body Problem. This problem models the Sun-Jupiter-Asteroid dynamics. For eccentricity of Jupiter \(e_0\) small enough, we show that there exists a family of probability measures supported at the \(3 : 1\) mean motion resonance such that the push forward under the associated Hamiltonian flow has the following property. At the timescale \(te_0^{-2}\), the distribution of the Jacobi constant of the Asteroid weakly converges to an Ito diffusion process on the line as \(e_0\to 0\). This resonance corresponds to the biggest of the Kirkwood gap on the Asteroid belt in the Solar System. This is a joint work with V. Kaloshin, P. Martin and P. Roldan. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it
Martedì 21 gennaio 2025
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
MDN Seminars
Elia Onofri (IAC-CNR)
On the Modelling of Granuloma-Like Structures: An Overview from In-Vitro to In-Silico Modelling
In 2024, tuberculosis remains a formidable global health challenge, contributing to millions of deaths annually. Central to the pathology of this disease are granulomas – intricate structures formed by the immune system in response to Mycobacterium tuberculosis infection. While various animal models have been developed to elucidate the mechanisms of granuloma formation and development, none of them fully recapitulate the human disease. Additionally, the limited throughput of these models presents a significant obstacle to their application in drug development. In recent years, three-dimensional cell cultures, known as Granuloma-Like Structures (GLS), have emerged as a promising tool that balances the complexity of in vivo conditions with the practicality required for high-throughput drug screening. Despite these advantages, in vitro models still present challenges that hinder their use in large-scale testing. Issues such as reproducibility, time consumption, and the need for human interaction limit their scalability. Therefore, as part of the European Regimen Accelerator for Tuberculosis (ERA4TB) project, we are developing an in silico model designed to simulate and reproduce GLS. In this talk, we will present the scientific context of tuberculosis research and introduce our multiscale GLS model, which combines an agent-based microscopic simulation of immune-pathogen interactions at the cellular level with a PDE-based macroscopic simulation of cell signalling diffusion at the molecular level. In addition to describing the model, we will discuss its calibration against experimental data, highlighting both the challenges and innovative solutions related to data analysis and integration.
Martedì 21 gennaio 2025
Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Winter School on Variational and PDE's Methods in Geometric Analysis
Program:
- 9:30 González (Selected talk)
- 11:30 Pigati (Minicourse Part II)
- 14:00 Rivière (Minicourse Part II)
- 16:00 Cruz-Blázquez (Selected talk)
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
Mercoledì 22 gennaio 2025
Ore 16:00, Aula dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Operator Algebra Seminar
Alessandro Pizzo (University of Rome Tor Vergata)
A Theory of Quantum Jumps
Starting from the so-called ETH-Approach to Quantum Mechanics we describe fluorescence and the phenomenon of “quantum jumps” in idealized models of atoms coupled to the quantized electromagnetic field. In a limiting regime where the orbital motion of the atoms is neglected and the velocity of light tends to ∞ we derive explicit non-linear stochastic differential equations describing the effective time evolution of states of individual atoms. These equations give rise to a measure on state trajectories exhibiting quantum jumps. This measure is a quantum- mechanical analogue of the Wiener measure on Brownian paths encountered in the theory of diffusion. Joint work with J. Fröhlich and Z. Gang. The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page
Mercoledì 22 gennaio 2025
Ore 16:15, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Antonio Ponno (Università di Padova)
The Fermi-Pasta-Ulam-Tsingou problem: a challenge in mathematical physics
The so-called Fermi-Pasta-Ulam-Tsingou (FPUT) problem, in large, concerns the problem of the approach of a Hamiltonian system to the state of equilibrium predicted by statistical mechanics. More precisely, the question is whether an initial measure evolves, through the dynamics, and in some specific sense, into the micro-canonical one, and on which time-scale(s). Still in other words, the problem consists in characterizing the mixing properties of the Hamiltonian system at hand. Starting with the seminal paper of FPUT, and due to tradition and to the sake of simplicity, most of the studies in the literature concern the dynamics of classical, identical, interacting particle chains (one-dimensional systems), that for smooth interaction potentials are equivalent to perturbations of harmonic oscillators. The original, negative result obtained by FPUT, the lack of any trend to equilibrium observed within the available computation time, was named, after them, the FPUT paradox. The aim of the present communication is to show that there is no paradox at all. Depending on energy, number of particles and initial conditions, the Hamiltonian system examined can usually be regarded as some small perturbation of a suitable integrable system close to it. The observed dynamics of the system resembles then, for a while, that of its closest integrable approximation, to then detach from it on a possibly long time-scale, to eventually reach the expected equilibrium. The whole process is referred to, in jargon, as "thermalization", the paradox being resolved by the existence of a nontrivial, short term, close to integrable "pre-thermal" stage. Some quantitative results on particle chains will be reviewed, with a particular emphasis on the short term dynamics for long wave-length, low energy initial conditions, where Burgers turbulence plays an important role.
Per informazioni, rivolgersi a: basile@mat.uniroma1.it, domenico.monaco@uniroma1.it
Mercoledì 22 gennaio 2025
Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Winter School on Variational and PDE's Methods in Geometric Analysis
Program:
- 9:30 Rivière (Minicourse Part III)
- 11:30 Pigati (Minicourse Part III)
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
Giovedì 23 gennaio 2025
Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Winter School on Variational and PDE's Methods in Geometric Analysis
Program:
- 9:30 Millot (Selected talk)
- 11:30 Pigati (Minicourse Part IV)
- 14:00 Rivière (Minicourse Part IV)
- 16:00 Catino (Selected talk)
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
Venerdì 24 gennaio 2025
Ore 14:30, Aula D'Antoni , Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata"
DocTorV Seminar
Giusi Capobianco (Università degli Studi di Roma "Tor Vergata")
Math is hot: the burning algorithm in tropical geometry
Tropical geometry is a relatively new area in mathematics studying metric graphs using combinatorial methods. In this talk, I will present Dhar’s burning algorithm for metric graphs and discuss its underlying algebro-geometric meaning. Additionally, we will apply this algorithm to compute the fibres of the Abel-Prym map associated to graph covers. No prior background in algebraic geometry is needed for this talk, as I will introduce the key concepts the definition of Abel-Prym and give a construction of covers of graphs.
Per informazioni, rivolgersi a: doctorv.uniroma2@gmail.com
Venerdì 24 gennaio 2025
Ore 14:30, aula B, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di presentazione dei risultati di tesi
Graziano Surace (Sapienza Università di Roma)
Nuove tecnologie digitali per una didattica laboratoriale interdisciplinare
This research investigates the impact of digital technologies, with a particular focus on smartphones, in interdisciplinary secondary school math and physics labs through the lens of educational innovation. The objective is to explore how these devices can effectively integrate into the classroom, overcoming technological, cognitive, and institutional barriers, and contribute to meaningful learning. The educational potential of mobile devices as measurement tools is analyzed from an interdisciplinary perspective that uses mathematics to investigate and model physical laws.
Per informazioni, rivolgersi a: graziano.surace@uniroma1.it
Venerdì 24 gennaio 2025
Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Winter School on Variational and PDE's Methods in Geometric Analysis
Program:
- 9:30 Pigati (Minicourse Part V)
- 11:30 Rivière (Minicourse Part V)
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
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