Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 19-09-2022 al 25-09-2022
Martedì 20 settembre 2022
Ore 10:00, aula 1B1, Dipartimento SBAI, Sapienza Università di Roma
PhD Course
Masahiro Yamamoto (The University of Tokyo)
Inverse problems and time-fractional partial differential equations 2
We consider an initial boundary value problem for time-fractional diffusion-wave equation (in the following we refer to it as system (*)). The lectures aim at self-contained concise explanations for the fundamental theory for such problems and mathematical analysis of inverse problems. The idea of fractional derivatives dates back to Leibniz and there have been many works including by Abel, Riemann, Liouville. Now the system (*) is widely recognized as more feasible model for various phenomena such as anomalous diffusion in heterogeneous media, where the anomaly cannot be well interpreted by the classical advection. diffusion equation and the conventional models often provide wrong simulation results. Thus we have to exploit more relevant models because the issues are serious, for example, for the protection of the environments , and the mathematical researches should support such practical applications. For researches on inverse problems, we need also mathematical analyses for (*). Usually in practice, we are not a priori given coefficients and other quantities in (*). The inverse problems are concerned with parameter identification, and are essential for more accurate prediction or simulations of anomalous diffusion. Therefore mathematical researches should be done for both foundations of direct problems and applications to inverse problems for (*).
Per informazioni, rivolgersi a: francesco.petitta@uniroma1.it
Martedì 20 settembre 2022
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Stephan Gerster (Università dell'Insubria)
Feedback control for hyperbolic balance laws
Physical systems such as gas networks are usually operated in a state of equilibrium and one is interested in stable systems, where small perturbations are damped over time. This talk is devoted to the design of boundary controls of systems that are described by hyperbolic balance laws. An underlying tool for the study of these problems are Lyapunov functions that yield upper bounds on the deviation from steady states in suitable norms. Furthermore, numerical approaches and limits of stabilizability are discussed.
Per informazioni, rivolgersi a: carlini@mat.uniroma1.it
Mercoledì 21 settembre 2022
Ore 15:00, Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario
Karl-Henning Rehren (University of Göttingen)
LV formalism in perturbative AQFT
pAQFT defines nets of local algebras by a limiting construction with relative S-matrices. The latter can be constructed perturbatively from an interaction Lagrangian. In many instances, the construction can be improved by adding a total derivative to the interaction Lagrangian (which would have no effect in classical field theory). The LV formalism controls whether and how this modification affects the (relative) S-matrices and provides a tool to identify the local observables of the model.
Mercoledì 21 settembre 2022
Ore 16:15, aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario
Fausto Di Biase (Università "G. D'Annunzio" di Chieti-Pescara)
On the differentiation of integrals in measure spaces along filters
In 1936, R. de Possel observed that, in the general setting of a measure space with no metric structure, certain phenomena, relative to the differentiation of integrals, which are familiar in the Euclidean setting precisely because of the presence of a metric, are devoid of actual meaning. In this work, in collaboration with Steven G. Krantz, we show that, in order to clarify these difficulties,it is useful to adopt the language of filters, which has been introduced by H. Cartan just a year after De Possel's contribution.
Giovedì 22 settembre 2022
Ore 10:00, 1B1, Dipartimento SBAI, Sapienza Università di Roma
PhD Course
Masahiro Yamamoto (The University of Tokyo)
Inverse problems and time-fractional partial differential equations 3
We consider an initial boundary value problem for time-fractional diffusion-wave equation (in the following we refer to it as system (*)). The lectures aim at self-contained concise explanations for the fundamental theory for such problems and mathematical analysis of inverse problems. The idea of fractional derivatives dates back to Leibniz and there have been many works including by Abel, Riemann, Liouville. Now the system (*) is widely recognized as more feasible model for various phenomena such as anomalous diffusion in heterogeneous media, where the anomaly cannot be well interpreted by the classical advection. diffusion equation and the conventional models often provide wrong simulation results. Thus we have to exploit more relevant models because the issues are serious, for example, for the protection of the environments , and the mathematical researches should support such practical applications. For researches on inverse problems, we need also mathematical analyses for (*). Usually in practice, we are not a priori given coefficients and other quantities in (*). The inverse problems are concerned with parameter identification, and are essential for more accurate prediction or simulations of anomalous diffusion. Therefore mathematical researches should be done for both foundations of direct problems and applications to inverse problems for (*).
Per informazioni, rivolgersi a: francesco.petitta@uniroma1.it
Giovedì 22 settembre 2022
Ore 16:00, Aula B, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Storia della Matematica
Alberto Cogliati (Università di Pisa)
Dai gruppi di Lie al metodo dei riferimenti mobili: Élie Cartan e la geometria
differenziale
Il metodo dei riferimenti mobili rappresenta una delle eredità più significative dell’opera di Élie Cartan: esso costituisce il tratto distintivo del suo particolare approccio allo studio della geometria differenziale e insieme lo strumento tecnico privilegiato attraverso il quale il matematico francese poté ottenere fondamentali risultati nel campo della geometria riemanniana, degli spazi simmetrici, della teoria dei gruppi di Lie e della teoria delle connessioni. L'intervento si propone di descrivere il percorso storico che condusse Cartan alla elaborazione di questo metodo. Particolare attenzione sarà dedicata ad esaminare il ruolo che in tale processo rivestirono le ricerche di Cartan (1899-1909) nel campo dei sistemi differenziali esterni e della teoria dei gruppi di Lie infinito dimensionali.
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interessata. Le comunicazioni pervenute in ritardo saranno ignorate.
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