Notiziario Scientifico
Notiziario dei seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 4 al 10 dicembre 2017
Lunedì 4 dicembre 2017
Ore 14:15, aula di Consiglio
seminario di Analisi Matematica
Jean Van Schaftingen (Université Catholique de Louvain)
Uniform boundedness principle for Sobolev maps between manifolds
The classical uniform boundedness principle of Banach and Steinhaus for linear
operators between Banach spaces is a theorem that transforms a bound depending
on the point in the domain into a global uniform bound. The nonlinear
character of Sobolev spaces between manifolds makes it unapplicable in these
spaces. By relying on the structure of the domain of Sobolev maps, we have
obtained a quite general uniform boundedness principle for energies of Sobolev
maps, which allows us to recover known estimates and counterexamples for the
problems of weak-bounded approximation, of extension of traces, of lifting and
of superposition. The result covers fractional and first order Sobolev spaces.
Lunedì 4 dicembre 2017
Ore 14:30, aula Dal Passo, dipartimento di Matematica,
Università di Roma Tor Vergata, viale della Ricerca Scientifica 1
colloquium di dipartimento
Jean-Pierre Eckmann (Università di Ginevra)
A review of Heat Transport in Hamiltonian systems
For the last few years, I have studied questions of heat transport in finite systems,
made of N identical pieces. While none of the obvious physical ideas seem in reach of
serious mathematics, some intriguing facts start to become clearer. Namely, that
transport is hampered by metastable states. Over the years I have had pleasant
collaborations with many people: Claude-Alain Pillet, Luc Rey-Bellet, Lai-Sang Young,
Martin Hairer, Pierre Collet, Carlos Mejia- Monasterio, Noe Cuneo, and Gene Wayne.
Lunedì 4 dicembre 2017
Ore 14:30, aula 311, Università di Roma Tre,
largo san Leonardo Murialdo 1
seminario di Algebra Commutativa
Giulio Peruginelli (Università di Padova)
Domini di Prufer di polinomi a valori interi
Sia V un dominio di valutazione di rango 1 e campo dei quozienti K. Recentemente Loper e
Werner hanno caratterizzato le successioni pseudoconvergenti E = fsngn2N V nel senso di
Ostrowski per le quali l'anello dei polinomi a valori interi su E, ossia
Int(E;V)=ff2K[X]jf(E)Vg, e un dominio di Prufer. In particolare, il loro risultato mostra
che esistono sottoinsiemi E di V che non sono precompatti per cui Int(E;V) e Prufer (per
esempio, una successione pseudo-convergente E di tipo trascendentale e breadth ideal non zero).
In questo seminario si da una caratterizzazione esaustiva di quei sottoinsiemi S di V per cui
Int(S;V) e Prufer. Il risultato utilizza la nozione di successione pseudo-monotona nel senso di
Chabert, che generalizza le successioni pseudo-convergenti. Si dimostra che Int(S;V) e di Prufer
se e solo se non esiste alcun elemento nella chiusura algebrica di K che sia uno pseudo-limite di
una successione pseudo-monotona in S, rispetto ad una opportuna estensione di V.
Martedì 5 dicembre 2017
Ore 14:30, aula Dal Passo, dipartimento di Matematica,
Università di Roma Tor Vergata, viale della Ricerca Scientifica 1
seminario di Equazioni Differenziali
Jessica Elisa Massetti (Università di Roma Tre)
Almost-periodic tori for the nonlinear Schrödinger equation
The problem of persistence of invariant tori in infinite dimension is a challenging problem in the
study of PDEs. There is a rather well established literature on the persistence of n-dimensional invariant
tori carrying a quasi-periodic Diophantine flow (for one-dimensional system) but very few on the persistence
of infinite-dimensional ones. Inspired by the classical 'twisted conjugacy theorem' of M. Herman for
perturbations of degenerate Hamiltonians possessing a Diophantine invariant torus, we intend to present
a compact and unified frame in which recover the results of Bourgain and Poschel on the existence of
almost-periodic solutions for the Nonlinear Schrödinger equation. We shall discuss the main advantages
of our approach as well as new perspectives. This is a joint work with L. Biasco and M. Procesi.
Mercoledì 6 dicembre 2017
Ore 11:00, aula riunioni (primo piano), IAC-CNR, via dei Taurini 19
seminario
Giovanni Sebastiani (IAC-CNR)
Analysis of seismic data from three recent earthquakes in the Appennines (Italy)
Some results of the statistical analysis of seismic data from the
earthquakes of Amatrice-Norcia-Campotosto (2016-17), L'Aquila (2009)
and Colfiorito (1997-98) are illustrated and discussed. The spatio-temporal
properties of seismic events following a mainshock (aftershocks) are investigated.
Mathematical Morphology and non parametric statistics are used to reduce
the effect of spatial noise. Parametric analysis in time domain and spectral
analysis are performed. The probabilistic properties of inter-arrival times of
aftershocks are also studied. The results obtained show evidence of two
different kinds of aftershock sequences. A possible interpretation of this fact
in terms of the geological properties of the spatial regions involved is discussed.
Furthermore, the evidence provided suggests the development of local
stochastic models based on non-stationary process, e.g. the Hawkes process.
This work is in collaboration with Dr. Aladino Govoni and Dr. Luca Pizzino of
the Istituto Nazionale di Geofisica e Vulcanologia (INGV).
Mercoledì 6 dicembre 2017
Ore 16:00, aula 311, Università di Roma Tre,
largo san Leonardo Murialdo 1
seminario di Analisi Matematica
Stefano Pasquali (Università di Roma Tre)
Dynamics of the nonlinear Klein-Gordon equation in the
nonrelativistic limit
We study the the nonlinear Klein-Gordon (NLKG) equation on a manifold M in the
nonrelativistic limit (as the speed of light c→∞).
We consider a higher-order normalized approximation of NLKG (corresponding to the NLS
at order r=1), and prove that when M is a smooth compact manifold or Rd,
the solution of the approximating equation approximates the solution of the NLKG locally
uniformly in time. When M=Rd, d≥2, we prove that for r≥2 small
radiation solutions of the order r normalized equation approximate solutions of the nonlinear
NLKG up to times of order cO(c2(r-1)).
Mercoledì 6 dicembre 2017
Ore 14:0, aula di Consiglio
seminario di Algebra e Geometria
Junyan Cao (Institut de Mathématiques de Jussieu)
A decomposition theorem for projective manifolds with nef anticanonical bundle
Let X be a simply connected projective manifold with nef anticanonical bundle. We prove that
X is a product of a rationally connected manifold and a manifold with trivial canonical bundle.
As an application we describe the MRC fibration of any projective manifold with nef anticanonical
bundle. It is a joint work with Andreas Horing.
Mercoledì 6 dicembre 2017
Ore 16:15, aula di Consiglio
seminario di Fisica Matematica
Giovanna Marcelli (Sapienza Università di Roma)
Spin Conductance and Spin Conductivity in Topological Insulators:
Analysis of Kubo-like terms
The last few decades witnessed an increasing interest, among solid state physicists, for physical
phenomena having a topological origin. This interest traces back to the milestone paper by Thouless,
Kohmoto, Nightingale and den Nijs on the Quantum Hall Effect (QHE), and involves the seminal papers
by Fu, Kane and Mele concerning the Quantum Spin Hall Effect (QSHE) to further developments in the
flourishing field of topological insulators.
As well known, in the QHE a topological invariant (Chern number) is related to an observable quantity,
the charge (Hall) conductance. By analogy, in the context of the QSHE, one would like to connect the
relevant topological invariant (Fu-Kane-Mele index) to a macroscopically observable quantity.
The natural candidates are spin conductance and spin conductivity, which in general are not equivalent.
As a paradigmatic case, we will analyse Kubo-like terms for spin conductance and spin conductivity in
a discrete two-dimensional model. In view of the continuity equation for spin transport, derived from
the first principles of Quantum Mechanics, our physical intuition suggests that spin conductance equals
the spin conductivity whenever the spin torque mesoscopic mass vanishes. Indeed, we will prove the
previous statement, as far as Kubo-like terms are concerned. To achieve the goal we first introduce
the definition of the principal value trace and of the j-principal value trace (for j∈{1,2}),
and then develop a suitable machinery to compute them.
The seminar is based on joint work with Gianluca Panati and Clement Tauber.
Giovedì 7 dicembre 2017
Ore 11:00, aula 211, Università di Roma Tre,
largo san Leonardo Murialdo 1
seminario di Logica e Informatica
José C. Valverde (Università di Castiglia-La Mancia)
Periodic structure of graph dynamical systems on maxterm and
minterm Boolean functions
The emergence of the concepts of cellular automata (CA) (Wolfram, 1983, 1984, 1986) and
Boolean (BN) network (Kauffman, 1969), between the end of the 60s and early 80s, for the
formalization of computational processes and genetic regulation, respectively, was a
first step in the development of modeling of evolutionary phenomena
using networks. This type of modeling has been useful to solve various
problems in other Sciences such as Chemistry (see Kier & Seybold,
2009; Kier, Seybold & Cheng 2005; Scalise & Schulman, 2015), Physics
(see Chopard & Droz, 1998), Biology (see Deutsch & Dormann, 2004,
Toroczkai & Guclu, 2007), Ecology (see Dieckman, Law & Metz, 2000;
Hofbauer & Sigmund, 2003; Hogeweg, 1988), even of Social Sciences like
Psychology or Sociology (see Abraham, 2015; Kempe, Kleminberg &
Tardos, 2005).
This new paradigm of modeling has evolved in recent years, giving rise
to the concept of graph dynamical system (GDS), which generalizes the
previous ones, since it contemplates that the relationships among
elements of the system can be arbitrary. That is, the graph
representing the relations among elements of the system, called
dependency graph, could be arbitrary. In this generalization, the
smallest units of aggregation of the phenomenon are called nodes (or
vertices), in relation to their membership in the graph, relieving the
term of cells in a CA and entities in a BN.
In this talk, we discuss some of the advances in the study of the
periodic structure of a GDS when the evolution operator is a maxterm
or minterm Boolean function.
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