Notiziario Scientifico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma
Settimana dal 29-06-2020 al 05-07-2020
Martedì 30 giugno 2020
Ore 14:30, Aula III e in videoconferenza Google Meet, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Dipartimento
Antonio Siconolfi (Sapienza Università di Roma)
Applicazioni della teoria KAM debole
Il seminario mira a dare una panoramica sulla Teoria KAM debole dalla sua nascita alla fine degli anni 90 dello scorso secolo sino ai più recenti sviluppi ed applicazioni. Si tratterà soprattutto il caso in cui le Hamiltoniane in considerazione abbiano bassa regolarità, in particolare non siano di tipo Tonelli, cioè di classe C2 e strettamente convesse, per cui un flusso Hamiltoniano non può essere definito. Si parlerà di applicazioni a vari problemi asintotici, dalla omogeneizzazione al fattore di sconto evanescente, e di impatto della teoria nello studio dei sistemi di equazioni di Hamilton–Jacobi, dell'analisi di problemi differenziali su grafi e networks, sino ai suoi collegamenti ai modelli di Mean Field Games.
Martedì 30 giugno 2020
Ore 14:30, On-line (via Microsoft Teams), Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Equazioni differenziali
Tere M-Seara (UPC Barcelona)
Breakdown of small amplitude breathers for the reversible Klein-Gordon equation
Instructions: the Seminar will be held in streaming, as a videoconference on-line, via Microsoft Teams. Link
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it
Martedì 30 giugno 2020
Ore 15:30, ZOOM Meeting ID: 962 612 6392 Pwd: mdn306, DIpartimento di Matematica, SAPIENZA
Seminario di Modellistica Differenziale Numerica
Dante Kalise (Nottingham University)
Sparse polynomial regression for optimal feedback laws
In this talk, we discuss a data-driven regression framework for the computation of high-dimensional optimal feedback laws. We propose a causality-free approach for approximating the value function of deterministic control problems via Pontryagin's Maximum Principle. A cloud of open-loop solves and the augmented information from the adjoints are used to perform a LASSO regression for a polynomial model of the value function. This allows to compute a reduced complexity representation of the optimal feedback map.
Per informazioni, rivolgersi a: falcone@mat.uniroma1.it
Mercoledì 01 luglio 2020
Ore 15:00, In streaming al seguente: indirizzo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Colloquium di dipartimento
Michael GHIL (ENS & PSLU Paris - UCLA Los Angeles)
Nonautonomous and Random Dynamical Systems in the Climate Sciences
H. Poincaré already raised doubts about the predictability of weather due to the divergence of orbits of dynamical systems associated more recently with chaos. Progress in the theory of nonlinear, deterministic dynamical systems (DDS theory) and the work of E. N. Lorenz justified Poincaré’s doubts. The theory of autonomous DDSs, with time-independent forcing and coefficients, provided a solid mathematical basis for the work on weather predictability over several decades. More recently, an interesting convergence occurred between studies of climate predictability and the development of the theory of nonautonomous and random dynamical systems (NDS and RDS). The diurnal and the seasonal cycle of insolation played a somewhat limited role in weather predictability for 10–15 days, but it became impossible to ignore the role of the seasonal cycle and of anthropogenic effects in climate predictability for years to decades. At the same time, the theory of purely deterministic, skew product flows, as well as that of RDSs, incorporated time-dependent forcing and coefficients and took huge mathematical strides, including the rigorous formulation and application of pullback attractors. A parallel development formulated and applied the concept of snapshot attractors. I will present some of the mathematical background and applications to the climate sciences, including: (i) the use of pullback and snapshot attractors for the proper understanding of the effects of time-dependent forcing upon intrinsic climate variability; (ii) the use of Wasserstein distance between time-dependent invariant measures to estimate these effects; (iii) the topological aspects of nonautonomous effects upon the intrinsic variability; and (iv) a “grand unification” between the nonlinear, deterministic and autonomous point of view and the linear, stochastically driven one.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006.
Per informazioni, rivolgersi a: molle@mat.uniroma2.it
Mercoledì 01 luglio 2020
Ore 17:00, On line seminar, Web site for information: https://www.dinamici.org/dai-seminar/
DinAmicI: Another Internet Seminar (DAI Seminar)
Marta Maggioni (Universiteit Leiden (Netherlands))
Matching for random systems with an application to minimal weight expansions
We consider families of skew-product maps, representing systems evolving in discrete time in which, at each time step, one of a number of transformations is chosen according to an i.i.d process and applied. We extend the notion of matching for such dynamical systems and we show that, for a certain family of piecewise affine random maps of the interval, the property of random matching implies that any invariant density is piecewise constant. We give an application by introducing a one-parameter family of random maps generating signed binary expansions of numbers. This family has random matching for Lebesgue almost every parameter, producing matching intervals that are related to the ones obtained for the Nakada continued fraction transformations. We use this property to study the expansions with minimal weight. Joint with K. Dajani, and C. Kalle. Note: The zoom link to the seminar will be posted on https://www.dinamici.org/dai-seminar/ and on https://mathseminars.org/seminar/DinAmicI. Moreover, it will be streamed live on youtube via the DinAmicI channel: https://www.youtube.com/channel/UCyNNg155G3iLS7l-qZjboyg
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it
Venerdì 03 luglio 2020
Ore 15:00, Modalità telematica, Dipartimento di Matematica e Fisica, Università degli Studi RomaTre
Seminario di Logica e Informatica Teorica
Francesco Pasquale (Università Tor Vergata)
Stabilization and expansion of simple dynamic random graph models for Bitcoin-like unstructured P2P networks
The Bitcoin P2P network is formed by thousands of nodes running the Bitcoin protocol. While the nodes participating in the network are mostly known, the peer discovery process in the protocol is explicitly designed to hide the global network structure. In this talk, we present a simple dynamic random graph model inspired by the peer discovery process in the Bitcoin protocol and we analyze its robustness with respect to stabilization and expansion: We show that the network dynamics quickly converges to a stable random graph that turns out to be a good expander, with high probability. The talk is based on joint work with Luca Becchetti, Andrea Clementi, Emanuele Natale, and Luca Trevisan.
Per partecipare al seminario cliccare sul seguente link: https://bit.ly/2AWogQ0
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