Notiziario Scientifico

Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma

Settimana dal 03-02-2025 al 09-02-2025

Lunedì 03 febbraio 2025
Ore 15:00, Aula 1B, RM002, Dipartimento SBAI
Corso di dottorato
Adriano Barra (Sapienza)
Neural Networks & Machine Learning
Timetable: February, every Mon, Wed and Fri (with two exceptions) at 15:00 in Room 1B, RM002, SBAI Department. After a streamlined historical introduction (e.g. the Turing machine, Rosenblatt's perceptron and AI’s winter time), the course focuses on the information processing capabilities of modern neural networks, both those biologically inspired (e.g. the Hopfield model and its variations on the theme) as well as those not-biologically driven (Boltzmann machines and feed-forward networks), with the related algorithms for learning and automatic recognition (e.g., Hebbian learning, contrastive divergence, back -prograpation, etc.). The methodological tools will be heavily based on the statistical mechanical formalization of neural networks and they will be discussed in every detail to inspect their emergent properties (i.e. those not immediately deductible by looking at the behavior of a single neuron). Specifically, we will try to understand how these networks are able to learn and abstract by looking at supplied examples from the external world and how, subsequently, they use what they have learned to respond appropriately, if stimulated, to the external world. We will also understand how these neural networks can sometimes make mistakes, and why.
Per informazioni, rivolgersi a: adriano.barra@uniroma1.it

Lunedì 03 febbraio 2025
Ore 17:00, aula Picone, Dipartimento di Matematica
Seminari Matematica Scienza e Società
Angelo Vulpiani (Sapienza Università di Roma)
Previsioni ed inferenza: dai dati ed i modelli all'intelligenza artificiale
Si discute la rilevanza dei modelli, i dati ed i metodi dell'intelligenza artificiale nei problemi di previsioni ed inferenza in fisica. Le principali difficoltà nella trattazione di tali problemi sono dovute alla possibile presenza del caos, l'esistenza di tante variabili con scale di tempo molto diverse e soprattutto una comprensione non accurata della dinamica dei fenomeni. E' interessante la rilevanza di risultati classici come il teorema di ricorrenza di Poincaré e il lemma di Kac.
Per informazioni, rivolgersi a: enrico.rogora@uniroma1.it

Lunedì 03 febbraio 2025
Ore 9:30:, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Rom
Winter School on Geometric Flows and Evolution Equations in Geometric Analysis
9:30 Otto (Minicourse Part I) 11:30 Laux (Selected talk) 14:30 Morini (Minicourse Part I) See https://sites.google.com/uniroma1.it/cvga2025/2nd-school for more information. This school is part of the activities of the Excellence Department Project CUP B83C23001390001 and it is funded by the European Union – Next Generation EU through PRIN 2022 J4FYNJ - CUP B53D23009320006, PRIN 2022 PJ9EFL - CUP B53D23009390006 and Progetto di Ricerca Ateneo De Marchis 2021, Sapienza Università di Roma.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it

Martedì 04 febbraio 2025
Ore 10:30, sala conferenze, INdAM Piazzale Aldo Moro, 5 – Roma
LYSeMinar
Alessandro Giuliani, Fédéric Patras, Thierry Paul (LYSM)
Special issue of LYSeMinar: MATINÉE QUANTIQUE

Per informazioni, rivolgersi a: https://www.altamatematica.it/lysm/lyseminar/

Martedì 04 febbraio 2025
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
Paolo Albano (Università di Bologna)
On the unique continuation for degenerate elliptic operators
We discuss the unique continuation property for linear differential operators of the form sum of squares of vector fields satisfying Hörmander's bracket generating condition. We provide some negative and some positive results.
NB:This talk is part of the activity of the MUR Excellence Department Project MATH@TOV CUP E83C23000330006
Per informazioni, rivolgersi a: molle@mat.uniroma2.it

Martedì 04 febbraio 2025
Ore 14:30, aula d'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Thomas Blomme (Université de Genève)
A short proof of the multiple cover formula
Enumerating genus g curves passing through g points in an abelian surface is a natural problem, whose difficulty highly depends on the degree of the curves. For "primitive" degrees, we have an easy explicit answer. For "divisible" classes, such a resolution is quite demanding and often out of reach. Yet, the invariants for divisible classes easily express in terms of the invariants for primitive classes through the multiple cover formula, conjectured by G. Oberdieck a few years ago. In this talk, we'll show how tropical geometry enables to prove the formula without any kind of concrete enumeration.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com

Martedì 04 febbraio 2025
Ore 9:30:, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Winter School on Geometric Flows and Evolution Equations in Geometric Analysis
9:30 Sire (Selected talk) 11:00 Morini (Minicourse Part II) 14:30 Otto (Minicourse Part II) 16:30 (Selected talk) See https://sites.google.com/uniroma1.it/cvga2025/2nd-school for more information. This school is part of the activities of the Excellence Department Project CUP B83C23001390001 and it is funded by the European Union – Next Generation EU through PRIN 2022 J4FYNJ - CUP B53D23009320006, PRIN 2022 PJ9EFL - CUP B53D23009390006 and Progetto di Ricerca Ateneo De Marchis 2021, Sapienza Università di Roma.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it

Mercoledì 05 febbraio 2025
Ore 14:00, Aula Dal Passo, Dipartimento di Matematica, Tor Vergata
Seminario
Stefano Favaro (Università di Torino)
A smoothed-Bayesian approach to frequency recovery from sketched data
We introduce a novel statistical perspective on a classical problem at the intersection of computer science and information theory: recovering the empirical frequency of a symbol in a large discrete dataset using only a compressed representation, or sketch, obtained via random hashing. Departing from traditional algorithmic approaches, recent works have proposed Bayesian nonparametric (BNP) methods that can provide more informative frequency estimates by leveraging modeling assumptions on the distribution of the sketched data. In this paper, we propose a smoothed-Bayesian method, inspired by existing BNP approaches but designed in a frequentist framework to overcome the computational limitations of the BNP approaches when dealing with large-scale data from realistic distributions, including those with power-law tail behaviors. For sketches obtained with a single hash function, our approach is supported by frequentist guarantees, including unbiasedness and optimality under a squared error loss function within a class of linear estimators. For sketches with multiple hash functions, we introduce an approach based on multi-view learning to construct computationally efficient frequency estimators. We validate our method on synthetic and real data, comparing its performance to that of existing alternatives. Joint work with Mario Beraha (Politecnico di Milano) and Matteo Sesia (University of Southern California)

Mercoledì 05 febbraio 2025
Ore 14:30, Aula B, Dipartimento di Matematica e Fisica, Università di Roma Tre, Via della Vasca Navale 84
Seminario di Fisica Matematica e Probabilità
Simone Baldassarri (Mathematical Institute Leiden University)
Opinion dynamics on dense dynamic random graphs
Describing the evolution of dynamic networks together with dynamic processes running on them constitutes a major challenge in network science. Despite considerable efforts in past years, and notable progress on an intuitive and approximative level, our mathematical understanding of such systems is still in its infancy. The focus of this talk will be two-opinion voter models on dense dynamic random graphs. The goal is to understand and describe the occurrence of consensus versus polarisation over long periods of time. The former means that all vertices have the same opinion, the latter means that the vertices split into two communities with different opinions and few disagreeing edges. We consider three models for the joint dynamics of opinions and graphs: one with one-way feedback and two with two-way feedback. In the first model only coexistence is attainable, meaning that both opinions survive, but with the presence of many disagreeing edges. In the second model only consensus prevails, while in the third model polarisation is possible. Key results cover functional laws of large numbers for the densities of the two opinions, functional laws of large numbers for the dynamic random graphs in the space of graphons, and a characterisation of the limiting densities in terms of Beta-distributions.

Mercoledì 05 febbraio 2025
Ore 16:15, Aula primo piano, IAC-CNR Roma
Seminario Volterra
Giada Basile (Sapienza Università di Roma)
Large deviations for binary collision models
Abstract. I will present some recent results on large deviations for binary collision stochastic models. The paradigmatic model is the Kac’s walk, described, in the kinetic limit, by the homogeneous Boltzmann equation. Although the dynamics preserves the energy, atypical paths that violate energy conservation may occur with exponentially small probability in the number of particles. I will exhibit a few examples of atypical paths with increasing/decreasing energy, and I will show that a dynamical phase transition may occur for the asymptotics of the total number of collisions. Finally, I will discuss an entropy dissipation inequality which involves the large deviation rate function. This is a joint work with L. Bertini, D. Benedetto, E. Caglioti and D. Heydecker. Founded by the European Union - Next Generation EU.

Mercoledì 05 febbraio 2025
Ore 9:30:, Sala di Consiglio", Dipartimento di Matematica, Sapienza Università di Roma
Winter School on Geometric Flows and Evolution Equations in Geometric Analysis
9:30 Otto (Minicourse Part III) 11:30 Morini (Minicourse Part III) See https://sites.google.com/uniroma1.it/cvga2025/2nd-school for more information. This school is part of the activities of the Excellence Department Project CUP B83C23001390001 and it is funded by the European Union – Next Generation EU through PRIN 2022 J4FYNJ - CUP B53D23009320006, PRIN 2022 PJ9EFL - CUP B53D23009390006 and Progetto di Ricerca Ateneo De Marchis 2021, Sapienza Università di Roma.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it

Giovedì 06 febbraio 2025
Ore 12:30, Aula Dal Passo, Dipartimento di Matematica, Università degli studi di Roma "Tor Vergata"
Seminario di Analisi Numerica
Stefano Pozza (Charles University)
How to express the solution of an ODE as a linear system (in a suitable algebra) and exploit it for fast computation and network analysis
The solution of systems of non-autonomous linear ordinary differential equations is crucial in various applications, such as nuclear magnetic resonance spectroscopy. We introduced a new solution expression in terms of a generalization of the Volterra composition. Such an expression is linear in a particular algebraic structure of distributions, which can be mapped onto a subalgebra of infinite matrices. It is possible to exploit the new expression to devise fast numerical methods for linear non-autonomous ODEs. As a first example, we present a new method for the operator solution of the generalized Rosen-Zener model, a system of linear non-autonomous ODEs from quantum mechanics. The new method’s computing time scales linearly with the model’s size in the numerical experiments. A second example is the analysis of temporal network, where the new expression might lead to novel extension of subgraph centrality indexes. Streaming link (MS Teams): https://teams.microsoft.com/l/meetup-join/19%3ad48916dee7364e0bbb08216ea621de47%40thread.tacv2/1738144836095?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%226f4c2a62-3ec4-4b20-9af3-43b578f2b18e%22%7d
Per informazioni, rivolgersi a: mariarosa.mazza@uniroma2.it

Giovedì 06 febbraio 2025
Ore 9:30:, Sala di Consiglio", Dipartimento di Matematica, Sapienza Università di Roma
Winter School on Geometric Flows and Evolution Equations in Geometric Analysis
9:30 Luckhaus (Selected talk) 11:00 Morini (Minicourse Part IV) 14:30 Otto (Minicourse Part IV) 16:30 De Gennaro (Selected talk) See https://sites.google.com/uniroma1.it/cvga2025/2nd-school for more information. This school is part of the activities of the Excellence Department Project CUP B83C23001390001 and it is funded by the European Union – Next Generation EU through PRIN 2022 J4FYNJ - CUP B53D23009320006, PRIN 2022 PJ9EFL - CUP B53D23009390006 and Progetto di Ricerca Ateneo De Marchis 2021, Sapienza Università di Roma.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it

Venerdì 07 febbraio 2025
Ore 16:00, Aula Enriques, Dipartimento di Matematica, Sapienza Università di Roma
Seminari PLS per docenti
Enrico Rogora (Sapienza Università di Roma) & Silvia Lanaro (Sapienza Università di Roma)
Costruzione dei poligoni regolari e soluzioni delle equazioni ciclotomiche

Per informazioni, rivolgersi a: annalisa.cusi@uniroma1.it

Venerdì 07 febbraio 2025
Ore 9:30:, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Winter School on Geometric Flows and Evolution Equations in Geometric Analysis
9:30 Morini (Minicourse Part V) 11:30 Otto (Minicourse Part V) See https://sites.google.com/uniroma1.it/cvga2025/2nd-school for more information. This school is part of the activities of the Excellence Department Project CUP B83C23001390001 and it is funded by the European Union – Next Generation EU through PRIN 2022 J4FYNJ - CUP B53D23009320006, PRIN 2022 PJ9EFL - CUP B53D23009390006 and Progetto di Ricerca Ateneo De Marchis 2021, Sapienza Università di Roma.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it

Le comunicazioni relative a seminari da includere in questo notiziario devono pervenire esclusivamente mediante apposita form da compilare online, entro le ore 24 del giovedì precedente la settimana interessata. Le comunicazioni pervenute in ritardo saranno ignorate. Per informazioni, rivolgersi all'indirizzo di posta elettronica seminari@mat.uniroma1.it.
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