Notiziario Scientifico
Settimana dal 11 al 17 maggio 2015
Lunedì 11 maggio 2015
Mercoledì 13 maggio 2015
Mercoledì 13 maggio 2015
Mercoledì 13 maggio 2015
Giovedì 14 maggio 2015
Giovedì 14 maggio 2015
Giovedì 14 maggio 2015
Giovedì 14 maggio 2015
Venerdì 15 maggio 2015
Venerdì 15 maggio 2015
Tutte le informazioni relative a questo notiziario devono pervenire
all'indirizzo di posta elettronica
seminari@mat.uniroma1.it
entro le ore 9 del venerdì precedente la settimana di pubblicazione.
Ore 14:30, aula di Consiglio
Seminario di Analisi Matematica e Probabilità
In the 80s, De Giorgi introduced the notion of abstract gradient
flows, which allowed to define a notion of solutions to ordinary
differential equations of the form x' = -grad F(x) on
metric spaces (rather than Riemannian manifolds for the usual
definition).
In 2005, Ambrosio, Gigli and Savare showed that when we consider
the space of probability measures on Rd
endowed with the Wasserstein metric, this notion allows to give
an alternate formulation for Fokker-Planck equations.
These equations are the PDEs
whose solutions are the flow of marginals of solutions of stochastic
differential equations of the form dX = -grad H(X)dt + dB.
In this talk, I will explain how we can use this notion to study large
deviations for sequences of SDEs. The main result is that proving a
large deviation principle is equivalent to studying the limit of a
sequence of functionals that appear in the abstract gradient flow
formulation for Fokker-Planck equations. As an application, I will
show how to obtain large deviations from the hydrodynamic scaling
limit for a system of interacting continuous spins in a random
environment.
Ore 11:00, aula 211, Unversità di Roma Tre
(largo s. Leonardo Murialdo)
Seminario di Probabilità
A central question in the study of disordered systems (and in
particular of their phase transition) is that of disorder relevance:
one wants to determine whether an arbitrarily small quantity of
disorder affects or not the critical behavior of the system. The
physicist Harris provided a simple and general criterion to know
whether disorder was relevant or irrelevant for a given d-dimensional
system.
In this talk, we will introduce the pinning model, a family of
disordered systems, which has attracted much attention in the past
decade: it considers a 1-dimensional polymer chain interacting with an
inhomogeneous defect line, undergoing a localization phase transition.
For this model, Harris' prediction has been rigorously proved, but the
marginal case (for which Harris criterion gives no prediction) was
partially left open. We will present here a necessary and sufficient
condition for disorder relevance for the pinning model, solving
completely the question for this model.
Ore 14:30, aula di Consiglio
Seminario di Algebra e Geometria
The representations of a quiver Q over a field k (the kQ-modules,
where kQ is the path algebra of Q over k) have been studied for
a long time, and one knows quite well the structure of the module
category Mod(kQ). It seems to be worthwhile to consider also
representations of Q over arbitrary finite-dimensional k-algebras A.
The lecture will draw the attention to the case when A=k[ε]
is the algebra of dual numbers (the factor algebra of the polynomial
ring k[T] in one variable T modulo the ideal generated by T2), thus
to the A-modules, where A=kQ[ε]=kQ[T]/
Ore 15:30, aula di Consiglio
Seminario di Algebra e Geometria
Ore 14:00, aula di Consiglio
Seminario P(n): Problemi Differenziali non Lineari
We present some recent results on the local boundedness and Lipschitz
continuity of weak solutions to quasilinear systems and/or local
minimizers to vector-valued integral functionals.
We consider systems and functionals under non standard p-q
growth conditions. Moreover, in this context the existence of weak
solutions is also examined.
Ore 14:00, aula 311, Unversità di Roma Tre
(largo s. Leonardo Murialdo)
Seminario di Probabilità
The hard disk model describes random configurations of disks in the
plane, interacting only via hard core exclusion. It is believed that
the model exhibits a weak form of crystallization for large activity
(i.e. high particle density). In spite of its simplicity, there are
only very few rigorous results on the hard disk model. I will present
a very recent result which can be interpreted as a lower bound on the
variance of particle positions in terms of the size of the system.
The result is obtained via a certain tansformation on particle
configurations. It builds on an earlier result concerning the
absence of positional order.
Ore 16:00, aula Zorzi, Unversità di Roma Tre (largo G.B. Marzi)
Seminario Formulas
Secondo MCA (studio del quale faccio parte come co-responsabile dell'area
ricerca e sviluppo), forme e materiali sono gli elementi principali
dell'architettura sostenibile. L'intento è di adattare le
soluzioni architettoniche alle condizioni ambientali così da
massimizzare il comfort interno minimizzando il ricorso all'impiantistica.
Una grande attenzione è rivolta quindi alla progettazione
dell'involucro architettonico.
La possibilità di controllare la geometria dell'edificio e della struttura
attraverso parametri ambientali (oltre che economici) è quindi
fondamentale nella metodologia di lavoro del nostro studio.
A volte geometrie più complesse possono essere anche più
efficienti, ma diventa fondamentale la capacità di gestire molte
variabili contemporaneamente all'interno di uno stesso modello;
comunicare e trasferire i dati a tutti gli attori del processo di
progettazione (strutturisti, impiantisti, ecc.); automatizzare il
più possibile la modellazione digitale dell'edificio in
funzione dei parametri di input; poter ottimizzare in qualunque
momento la geometria anche in funzione di dati non previsti inizialmente.
In altre parole progettare e modellare in maniera parametrica e con
strumenti e algoritmi personalizzabili.
Attraverso tre esempi rappresentativi delle tre diverse fasi di
progettazione: preliminare, definitiva ed esecutiva, proveremo ad
illustrare alcune applicazioni del metodo di progettazione parametrica
come strumento per ottimizzare il processo di progettazione, rendere
più efficiente l'edificio, e facilitarne la fase di costruzione.
Illustreremo:
1- un approccio di tipo generativo: variazione di una geometria per
massimizzare le superfici esposte ad illuminazione diretta per più
di 2 ore al giorno in inverno.
2- Modellazione e controllo geometrico di una facciata 'non standard',
estrapolazione e scambio di dati
3- Ottimizzazione strutturale di una griglia tridimensionale per ridurre
il numero di componenti e di nodi diversi tra loro
Ore 15:30, aula G
We discuss the measure of (Lagrangian) invariant tori in nearly-integrable
hamiltonian systems. It is well known in KAM theory that the measure of
the complementary of invariant tori (where chaotic motions possibly occur)
is smaller than the sqare root of ε, ε being the
perturbative parameter.
A conjecture by Arnold, Kozlov and Neishtadt claims that such
measure is actually of order ε. We prove that such conjecture
holds true for 'general' mechanical systems (namely systems of the form:
kinetic energy plus potential energy). Joint work with L. Chierchia.
Ore 10:30, stanza 34, Dipartimento di Scienze Statistiche
We give a quantitative Gaussian and Poisson approximation for the
first chaos (or innovation) of spatial point processes with conditional
intensity. To this aim we use a Malliavin-Stein-Chen approach. This
method is essentially based on the following two steps. First, we
provide an integration by parts (IBP) formula which relates the first
chaos with the discrete Malliavin operator. Second, we derive the
probability approximations by combining the IBP formula with the
Stein and Chen methods. Our findings extend the corresponding results
on the Poisson space due to Peccati, Solè, Taqqu and Utzet (2010)
and Peccati (2011). The general bounds presented in this talk are
applied to stationary, inhibitory and finite range Gibbs point
processes with pair potential, providing explicit error bounds
and quantitative limit theorems.
Ore 12:00, aula di Consiglio
Seminari MoMa
Engineering, intended as the capability of producing innovation
and new technology, pays an important tribute to mathematics.
It is well known how the increasing computer power open the door
to sophisticated models of physical and engineering systems.
But there is much more in engineering for the use of mathematics.
The word of new sensors, keeping information from the environment
(airplanes, cars, industrial plants to the human body) for monitoring
purposes to predict and prevent faults and dangerous scenarios through
data signal processing, is one of the challenging opportunity.
Special controls to realize new self-controlled devices or unmanned
vehicles is another exciting example. Probabilistic models for
optimizing the matching between technology performances and economics
is another aspect of valuable importance.
The seminar aims to provide a glimpse on the use of advanced
mathematics in the world of applications in industrial engineering,
through concrete examples on running projects.
Tutti coloro che desiderano ricevere questo notiziario via e-mail sono
invitati a comunicare il proprio indirizzo di posta elettronica a
seminari@mat.uniroma1.it.
Il Direttore