Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 13-02-2023 al 19-02-2023
Lunedì 13 febbraio 2023
Ore 11:00, Aula B, Dipartimento di Matematica, Università di Roma `La Sapienza'
Corso di Dottorato
Dario Trevisan
Mathematical aspects of Quantum Information Theory
Per informazioni, rivolgersi a: bertini@mat.uniroma1.it
Lunedì 13 febbraio 2023
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Felix Otto (MPI Leipzig)
The thresholding scheme for mean curvature flow and De Giorgi's ideas for gradient flows
The fact that the flow of a hypersurface by its mean curvature can be seen as a gradient flow of the surface area has motivated an influential minimizing movement scheme (Almgren-Taylor-Wang, Luckhaus-Sturzenhecker). Also Osher's computationally efficient and very popular thresholding scheme for mean curvature flow by Osher et. al. can be interpreted as a minimizing movement scheme (Esedoglu-O.).
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
Martedì 14 febbraio 2023
Ore 11:00, aula C, Dipartimento di Matematica
Seminari di Storia della Matematica
Riccardo Bellé
Galileo e il centro di gravità dei solidi
Galileo nei primi anni della sua carriera (1585-1588) si occupò della determinazione del centro di gravità di alcuni solidi. Si trattava di un tema che nel corso della seconda metà del XVI secolo aveva occupato studiosi del calibro di Francesco Maurolico, Federico Commandino e Cristoforo Clavio. Il giovane Galileo ottenne alcuni risultati interessanti che condivise con lo stesso Clavio e con Guidobaldo Dal Monte. Nel seguito, gli interessi di Galileo si allontanarono da questo genere di studi e i suoi scritti sul tema furono pubblicati solo nel 1638 (come appendice ai Discorsi e dimostrazioni matematiche intorno a due nuove scienze). Nel seminario prenderò in esame gli studi di Galileo sui centri di gravità dei solidi e sulla base del confronto tra le diverse versioni a nostra disposizione proporrò una loro possibile evoluzione.
Per informazioni, rivolgersi a: rogora@uniroma1.it
Martedì 14 febbraio 2023
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Probabilità
Luisa Andreis (Politecnico di Milano)
Rare events in sparse random graphs
Rare events for dense random graphs are well described using the theory of large deviations and graphons. When graphs are sparse the picture is less clear, objects that describe globally the graphs and their limits, as graphons do for dense graphs, have not been defined yet. Nevertheless we do have information on how these graphs look like when explored locally from a vertex and this, under some assumptions, gives also information on global properties. In this talk we will give an overview on what is known on rare events in this regime, focusing in particular on large deviation statements on connected components in inhomogeneous random graphs and on links with coagulation processes. This talk is based on joint works with Wolfgang König (WIAS and TU Berlin), Tejas Iyer, Heide Langhammer, Elena Magnanini and Robert Patterson (WIAS).
Martedì 14 febbraio 2023
Ore 14:30, aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Eleonora Romano (Università di Genova)
Recent results on Fano varieties
In this talk we present some recent results on complex smooth Fano varieties. To this end, we first recall an invariant introduced by Casagrande, called Lefschetz defect. We review the literature to deduce that all Fano manifolds with Lefschetz defect greater than three are well known. Then we focus on the case in which the Lefschetz defect is equal to three, by discussing a structure theorem for such varieties. As an application, we use this result to classify all Fano 4-folds with Lefschetz defect equal to three: there are 18 families, among which 14 are toric. This is a joint work with C. Casagrande and S. Secci.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Martedì 14 febbraio 2023
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Chiara Simeoni (University of Côte d'Azur)
Analysis and numerics of the propagation speed for hyperbolic reaction-diffusion models
We discuss models for reaction-diffusion phenomena based on hyperbolic equations. The standard approach uses parabolic systems, which are well suited to explain events such as heat transmission in close-to-equilibrium regimes, but are criticizable for several reasons (e.g. the prediction of infinite speed of propagation, the lack of time-delay and related inertial effects, and the exceptionality of well-posed boundary value problems). In many contexts the hyperbolic corrections are relevant for applications: dynamics of biological tissues, population growth, forest fire models. We adopt a description by means of hyperbolic models - starting from the basic example of telegraph equation - which are more appropriate when the relaxation time to perceive changes of the overall phenomenon is sufficiently large as compared to the diffusivity coefficient, and differences emerge in the transient regimes whose cumulations may influence significantly the final outcome. The emphasis is placed on the numerical computation of the propagation speed of special traveling wave solutions, i.e. propagating fronts. Three basic numerical schemes are presented, two of which can also be applied to general hyperbolic systems (with reduced performance when dealing with discontinuous initial data). We compare their performance for providing effective approximations of the propagation speed. We focus on a special class of 2x2 systems corresponding to second order PDEs in 1D as simplified modeling of reaction-diffusion equations with monostable and bistable reaction terms. Beside the phase-plane algorithm for hyperbolic reaction-diffusion systems with damping, we propose two PDE-based numerical schemes, the so-called scout&spot algorithm - based on tracking the level curve of some intermediate value of the wave profile - and the LeVeque-Lee formula - given by the average value of the discrete transport velocity - by assessing their capability in comparative experiments of genuine predictions.
Martedì 14 febbraio 2023
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Equazioni Differenziali
Lei Zhang (University of Florida)
Asymptotic behavior of solutions to the Yamabe equation in low dimensions.
In this talk I will report recent progress on the Yamabe equation defined either on a punctured disk of a smooth manifold or outside a compact subset of \( {\mathbb R}^n\) with an asymptotically flat metric. What we are interested in is the behavior of solutions near the singularity. It is well known that the study of the Yamabe equation is sensitive to the dimension of the manifold and is closely related to the Positive Mass Theorem. In my recent joint works with Jingang Xiong (Beijing Normal University) and Zhengchao Han (Rutgers) we proved dimension-sensitive results and our work showed connection to other problems.
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it
Mercoledì 15 febbraio 2023
Ore 10:00, Aula 6, edificio RM018 (aule di Ingegneria, Via del Castro Laurenziano), Dipartimento SBAI, Sapienza Università di Roma
Mini-corso
Felix Otto (MPI-MIS, Leipzig)
Stochastic homogenization and large-scale regularity
Lectures: (10/02 14:00,) 15/02 10:00, 17/02 14:00, 22/02 10:00, 24/02 14:00. Recording of previous lectures are expected to be available upon request. In this mini-course, I will introduce the concept of large-scale regularity in case of a linear elliptic equation (or system) with heterogeneous coefficients. It is based on a smallness (on average) of the potentials of the harmonic coordinates, and proceeds via an intrinsic Campanato iteration. I will then apply this to the case of a random heterogeneous coefficient field, sampled from a stationary and ergodic ensemble. I will try to be self-contained and closely follow Theorem 1 and Lemma 1 in Gloria, Neukamm, and Otto "A regularity theory for random elliptic operators", Milan J Math 2020.
Per informazioni, rivolgersi a: lorenzo.giacomelli@uniroma1.it
Mercoledì 15 febbraio 2023
Ore 14:00, Aula Dal Passo, Dipartimento di Matematica, Università Tor Vergata
Seminario RoMaDS
Francesco Vaccarino (Politecnico di Torino)
Hodge-Shapley game: a Laplacian-based Shapley-like associated game for eXplainable AI
In cooperative game theory, a set of players or decision-makers should negotiate to decide how to allocate the worth gained by the coalition composed of all the players. A value is a solution concept that suggests the outcome of the negotiation among players. Among the many existing alternative solution concepts, it is prevalent the Shapley value solution concept. Its popularity also derives from the property of being a fair allocation, where a set of desirable properties or axioms describes fairness. The axioms characterize the Shapley value in the sense that it is the unique value satisfying those properties; at the same time, the axioms allow deriving a simple explicit combinatorial formula to compute the Shapley value. In our approach, coalitions are the main subjects of cooperation, instead of single players, and, inspired by the Shapley value, the goal is to derive a fair associated game, i.e. an allocation to coalitions satisfying a set of desirable properties. The methodology is based on using the Hodge decomposition of the simplicial complex associated with the partially ordered set of the subsets of the set of players ordered by inclusion. We will motivate this investigation within the framework of Explainable Artificial Intelligence (XAI). Joint work with Antonio Mastropietro (Eurecom - F)
Per informazioni, rivolgersi a: salvi@mat.uniroma2.it
Mercoledì 15 febbraio 2023
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Giacomo Cherubini (INDAM / Sapienza Università di Roma)
Teorema delle geodetiche prime
C'è una curiosa analogia tra i numeri primi e le lunghezze delle geodetiche chiuse primitive ("prime") sulla superficie modulare. Nel seminario introdurrò le geodetiche in considerazione e cercherò di motivare tale somiglianza, visibile soprattutto nella loro distribuzione asintotica. Descriverò inoltre una formulazione equivalente che coinvolge il regolatore e il numero di classe di campi quadratici reali, entrambi di grande interesse aritmetico. Infine presenterò una congettura aperta sul risultato ottimale atteso per il termine di errore nel teorema delle geodetiche prime e progressi recenti verso tale risultato.
Mercoledì 15 febbraio 2023
Ore 14:15, online (zoom), disponibile alla pagina https://indico.gssi.it/event/410/
ciclo Mathematical Challenges in Quantum Mechanics
San Vũ Ngọc (Università di Rennes)
Normal forms for 1D Hamiltonians with A_k singularities: applications to inverse spectral theory
In the case of a Hamiltonian H with Morse singularities, old results allow us to establish the link between the geometry of the level surfaces and the precise distribution of the eigenvalues of the quantized H, which leads to a nice inverse result: recover the (symplectic) geometry from the semiclassical spectrum. In the case of degenerate singularities of type A_k (in Arnold's classification), we obtain with N. Martynchuk (Groningen) a more subtle classification (beyond action integrals), but we conjecture nevertheless that the inverse problem should be solvable.
Per informazioni, rivolgersi a: monaco@uniroma1.it
Mercoledì 15 febbraio 2023
Ore 14:30, Canale Youtube dell'IAC https://www.youtube.com/watch?v=y4emUAhUzTA, Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche
Online Seminars on Artificial Intelligence and Mathematics, 2023 Edition https://www.aim.iac.cnr.it/
Dario Pasquini (EPFL Lausanne)
Privacy-Preserving Collaborative Machine Learning?
Deep learning requires massive data sets to reach peak performance. Unfortunately, collecting suitable data sets is difficult or sometimes impossible. Entities and organizations may not be willing to share their internal data for fear of releasing sensitive information. For instance, telecommunication companies would benefit extraordinarily from deep learning techniques but do not wish to release customer data to their competitors. Similarly, medical institutions cannot share information because privacy laws and regulations shelter patient data. It is here that collaborative machine learning comes to our rescue. Collaborative machine learning protocols such as “Federated Learning” enable a set of parties to train a machine learning model in a distributed fashion. In the process, users’ private data remains local on their devices, ensuring that no private information is leaked, right? Well, that may not be strictly true. This talk is about misconceptions, inaccurate assumptions, unrealistic trust models, and flawed methodologies affecting current collaborative machine learning techniques. In the presentation, we cover different security issues concerning both emerging approaches and well-established solutions in the privacy-preserving collaborative machine learning landscape. The objective here is to highlight the general errors and flawed approaches we all should avoid in devising, implementing, and using "privacy-preserving collaborative machine learning”.
Per informazioni, rivolgersi a: roberto.natalini@cnr.it
Mercoledì 15 febbraio 2023
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Lorenzo Bertini Malgarini (Università di Roma La Sapienza)
Current fluctuations in stochastic lattice gases: Donsker-Varadhan meets Freidlin-Wentzell
We discuss the large deviations asymptotic of the time-averaged empirical current in stochastic lattice gases in the limit in which both the number of particles and the time window diverges. For some models it has been shown that dynamical phase transitions occur: the optimal density profile to realize such deviations is given by travelling waves rather than by homogeneous profiles. We shall prove a variational representation, proposed by Varadhan, for the corresponding rate function that is obtained by projecting the large deviations at the level of the empirical process.
Giovedì 16 febbraio 2023
Aula Gini, Dip. di Scienze Statistiche, Sapienza Università di Roma (piano terra dell'edificio CU002)
Workshop Dipartimentale - 1ª edizione
Metodi per la Conoscenza | Il Dipartimento di Scienze Statistiche si presenta
Schedule:
- 09:30 Marco Schaerf (Preside I3S), Saluti Istituzionali
- 10:00 Giovanna Jona Lasinio (Direttrice del DSS), Apertura Lavori
- 10:20 Fulvio De Santis e Valeria Sambucini, Contributi ai metodi bayesiani per disegno e analisi di prove cliniche
- 10:40 Susanna Levantesi, Strumenti avanzati per la valutazione del rischio in ambito attuariale
- 11:00 Maurizio Vichi, Clustering e riduzione dimensionale per dati complessi e loro applicazioni
- 11:20 Fiorenza Deriu, La Network Analysis nello studio delle reti di servizi: evidenze dell'Indagine network sui servizi di prevenzione e contrasto al disturbo da gioco d’azzardo nella Regione Lazio
- 11:40 coffee break
- 12:00 Paolo Dell'Olmo e Lavinia Amorosi, Avanzamenti delle tecniche di risoluzione dei problemi di ottimizzazione e applicazioni
- 12:20 Giulia Rotundo e Giacomo Morelli, Metodi quantitativi per la misurazione e la gestione dei rischi in ambito finanziario
- 12:40 Carlo D’Ippoliti, Gestire la complessità in economia
- 13:00 break (pranzo, Aula 2)
- 14:30 Luca Tardella e Cristina Mollica, Ranking data uncertainty and its use with sports data
- 14:50 Filomena Maggino, Statistica e la sfida della complessità sociale
- 15:10 Luisa Beghin, Modelli aleatori della realtà
- 15:30 coffee break
- 15:50 Elisabetta Barbi, La rivoluzione demografica
- 16:10 Bernardo Maggi, Eurosystem stability: a stochastic dynamic optimization approach to public debt
- 16:30 Paolo Franciosa, Algoritmi e metodi efficienti per l'analisi e la gestione dei dati
- 16:50 Giovanna Jona Lasinio, Dal mare alle montagne: la statistica e la natura
- 17:10 Discussione aperta
Webpage: https://www.dss.uniroma1.it/it/wsdss1
Zoom: https://uniroma1.zoom.us/j/96613351917
Per Informazioni: pierpaolo.brutti@uniroma1.it
Giovedì 16 febbraio 2023
Ore 14:00, Aula dei Seminari, Ed. RM004, Via Scarpa 16, Dipartimento SBAI, Sapienza Università di Roma
Seminario "PDE a tutto SBAI"
Francesco Della Pietra (Università degli studi di Napoli Federico II)
Problemi di ottimizzazione di forma in modelli per la trasmissione del calore
Nel seminario considereremo alcuni problemi di ottimizzazione di forma per equazioni ellittiche con condizioni al bordo di tipo Robin. Problemi di questo tipo, nel caso di condizioni di tipo Dirichlet, sono stati ampiamente studiati; noi ci occuperemo di condizioni al bordo di tipo Robin, perché siamo motivati dallo studio di alcuni modelli di trasmissione del calore in problemi di isolamento termico. Dopo aver illustrato alcuni modelli, considereremo questioni relative a all'ottimizzazione di forma. I risultati che descriveremo sono contenuti in lavori in collaborazione con Carlo Nitsch (UniNa), Riccardo Scala (UniSi) e Cristina Trombetti (UniNa).
Per informazioni, rivolgersi a: massimo.grossi@uniroma1.it
Giovedì 16 febbraio 2023
Ore 14:15, Aula M1, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Riccardo Salvati Manni (Sapienza)
Slope of Siegel modular forms: some geometric applications
We study the slope of modular forms on the Siegel space. We will recover known divisors of minimal slope for \(g\leq 5\) and we discuss the Kodaira dimension of the moduli space of principally polarized abelian varieties \(\mathcal{A}_g\) (and eventually of the generalized Kuga's varieties). Moreover we illustrate the cone of moving divisors on \(\mathcal{A}_g\). Partly motivated by the generalized Rankin-Cohen bracket, we construct a non-linear holomorphic differential operator that sends Siegel modular forms to Siegel cusp forms, and we apply it to produce new modular forms. Our construction recovers the known divisors of minimal moving slope on \(\mathcal{A}_g\) for small genera.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
Giovedì 16 febbraio 2023
Ore 15:00, Aula C (il seminario potrà essere seguito anche tramite Zoom), Dipartimento di Matematica, Sapienza Università di Roma
Seminari di Ricerca in Didattica della Matematica
Marta Menghini (Sapienza Università di Roma)
Dalla geometria pratica al metodo laboratoriale: un excursus storico
Per seguire il seminario a distanza, rivolgersi a annalisa.cusi@uniroma1.it
Venerdì 17 febbraio 2023
Ore 11:00, Aula B, Dipartimento di Matematica, Università di Roma `La Sapienza'
Corso di Dottorato
Dario Trevisan
Mathematical aspects of Quantum Information Theory
Per informazioni, rivolgersi a: bertini@mat.uniroma1.it
Venerdì 17 febbraio 2023
Ore 11:30, Aula Seminari edificio RM004, Dipartimento di Scienze di Base e Applicate per l'Ingegneria
seminario di Analisi Matematica
Masahiro Yamamoto (The University of Tokyo)
Case studies for solutions of real-world problems by mathematical thinking from steel industry to environmental issues
There is an opinion that mathematics is a pure and abstract discipline of natural sciences, and must be even far away from the real-world issues. On the other hand, mathematics is useful for solving real-world problems around us and is nothing but one convenient tool. I think that both views are too extreme: I would like to demonstrate that it is important that we keep both characters of mathematics as abstract discipline and as useful methods for real-world issues, in order to develop mathematics itself and exert the full power of mathematics for solving practical problems. Mathematics is not only abstract, but is also strong engine for solving concrete problems and creates huge economic effects and serves for the public welfare. Moreover we have witnessed that such application-oriented researches of mathematics have widened and deepened related mathematical theories themselves. In order to understand such aspects, I will describe several applications of mathematics to real-world problems by case studies where I have been working. The case studies include - From iron-making industry: monitoring method for the interior of a blast furance based on inverse problems - Underground diffusion of cesium 137 in the soil after Fukushima Nuclear Disaster: decontamination of farmlands - Time-fractional diffusion equations: recent example of mathematics inspired by real-world problem - Process design for better tasting of cup-noodles: trial without modelling
Venerdì 17 febbraio 2023
Ore 14:00, Aula 6, edificio RM018 (aule di Ingegneria, Via del Castro Laurenziano), Dipartimento SBAI, Sapienza Università di Roma
Mini-corso
Felix Otto (MPI-MIS, Leipzig)
Stochastic homogenization and large-scale regularity
Lectures: (10/02 14:00, 15/02 10:00,) 17/02 14:00, 22/02 10:00, 24/02 14:00. Recording of previous lectures are expected to be available upon request. In this mini-course, I will introduce the concept of large-scale regularity in case of a linear elliptic equation (or system) with heterogeneous coefficients. It is based on a smallness (on average) of the potentials of the harmonic coordinates, and proceeds via an intrinsic Campanato iteration. I will then apply this to the case of a random heterogeneous coefficient field, sampled from a stationary and ergodic ensemble. I will try to be self-contained and closely follow Theorem 1 and Lemma 1 in Gloria, Neukamm, and Otto "A regularity theory for random elliptic operators", Milan J Math 2020.
Per informazioni, rivolgersi a: lorenzo.giacomelli@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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