Notiziario Scientifico
Settimana dal 24 al 30 novembre 2014
Lunedì 24 novembre 2014
Martedì 25 novembre 2014
Martedì 25 novembre 2014
Martedì 25 novembre 2014
Mercoledì 26 novembre 2014
Mercoledì 26 novembre 2014
Mercoledì 26 novembre 2014
Mercoledì 26 novembre 2014
Giovedì 27 novembre 2014
Giovedì 27 novembre 2014
Giovedì 27 novembre 2014
Giovedì 27 novembre 2014
Venerdì 28 novembre 2014
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
Biagio Cassano
Scattering in the energy space for nonlinear Schrödinger equations.
We study the theory of Scattering in the energy space for various nonlinear Schrödinger equations.
In dimension 3 or bigger we consider a variable coefficients equation, for a gauge invariant,
defocusing nonlinearity of power type on an exterior domain with Dirichlet boundary conditions. In
order to prove scattering, we prove a bilinear smoothing (interaction Morawetz) estimate for the
solution and, under the conditional assumption that Strichartz estimates are valid for the linear
flow, we prove global well posedness in the energy space for energy subcritical powers, and
scattering provided the power is mass supercritical. When the domain is the whole space, by
extending the Strichartz estimates due to Tataru, we prove that the conditional assumption is
satisfied and deduce well posedness and scattering in the energy space. In low dimension spaces of
dimension 1,2 or 3, we simplify the scattering theory in R^n for the Schrödinger equation,
generalizing it to the system framework. Joint work with Piero D'Ancona and Mirko Tarulli.
Thuong Nguyen
Asymptotic Behavior of Singularly Perturbed Control System: non-periodic setting
(joint work with Antonio Siconolfi)
In this talk we are interested in asymptotic behavior of singularly perturbedcontrol system in the
non-periodic setting. More precisely, we consider the value function of finite horizon optimal
control problem (Bolza form) associated with singularly perturbed control system, and aim at
characterizing its weak semilimits as viscosity sub- and supersolutions of a limiting
Hamilton-Jacobi-Bellman equation (also called eu21b5ective HJB equation). This PDE approach is
extensively studied in a series of papers by Alvarez & Bardi in the periodic setting ([AB03],
[AB10]). Our contribution is to extend the results of Alvarez & Bardi to the nonperiodic case. The
key idea is to replace the periodicity on the datum by coercivity on the running cost, and we only
need the local version of boundedtime controllability used in [AB10]. The remarkable novelty of our
work is to approximate the Bellman Hamiltonian (convex, but non-coercive in the momentum) by a
suitable sequence of convex, coercive Hamiltonians and then use some basic tools of Aubry-Mather
theory developed by Fathi & Siconolfi (see [FS05]) for these convex, coercive Hamiltonians. We
finally obtain some similar results as those of Alvarez & Bardi. [AB03] O. Alvarez, M. Bardi,
Singular perturbations of nonlinear degenerate parabolic PDEs: a general convergence result. Arch.
Ration.Mech. Anal. 170 (2003), no. 1, 17-61.
[AB10] O. Alvarez, M. Bardi, Ergodicity, stabilization, and singular perturbations for
Bellman-Isaacs equations. Mem. Amer. Math. Soc. 204 (2010), no. 960.
[FS05] A. Fathi, A. Siconolfi (2005), PDE aspects of Aubry-Mather theory for quasiconvex
Hamiltonian, Calc. Var. 22, 185-228.
Ore 14:30, Aula Dal Passo, Università di Roma II
Seminario di Equazioni Differenziali
We present a new method to establish the rotational symmetry of solutions to overdetermined elliptic
boundary value problems. We illustrate this approach through a couple of classical examples arising
in potential theory as well as in the study of static metrics in General Relativity.
Ore 15:00, Aula Picone
Seminario di Algebra e Geometria
We will introduce our recent results on the use of persistent homology in the field of complex
networks. In particular we will show how persistence homology can be used to discriminate the
variation of the brain functional connectome under the influence of psilocybin extracted from magic
mushrooms. We, furthermore give account of our theorem which shows that a persistence module on a
finite poset P can be obtained from the filtration of a graph weighted over P.
Ore 15:00, Aula di Consiglio
Seminario di Modellistica differenziale numerica
In questo seminario presenterò una nota approssimazione semi-Lagrangiana per equazioni di
Hamilton-Jacobi del secondo ordine, introducendo alcune modifiche e combinando alcuni concetti
chiave che permettono di accelerare notevolmente il calcolo della soluzione numerica: eliminazione
dell'auto-dipendenza, causalità, condizione di diffusione upwind. Illustrerò quindi i risultati di
diversi esperimenti numerici, ottenuti implementando il metodo proposto in un codice parallelo.
Ore 10:00, Aula 1B1, Dipartimento SBAI
The talk has two remotely connected parts: Firstly, we present a continuum PDE-ODE model for
collagen self-assembly describing the interplay between the change in the polymer distribution and
the evolution of monomers. We endow the model with periodic coefficients, where the small parameter
is interpreted in this context as the ratio of lengths of monomers and fibrils. After applying a
fixed-point homogenization argument and proving corrector estimates, we use the microscopic
information incorporated in the first order correctors to explain the so-called turbidity
measurement. Secondly, we present a PDE model for the continuum motion of populations of hot
colloidal particles at the pore scale inside a heterogeneous (periodic or locally-periodic) porous
material. The focus is now on deriving macroscopic equations and the corresponding effective
transport coefficients that account for the intimate interplay between the Smoluchowski aggregation
and dissolution of size classes and the deposition of the biggest colloid populations on the pores
surface in the presence of diffusion/dispersion. To reach this goal, we combine gradient-like
estimates for both the temperature and the concentration of colloidal populations with the concept
of two-scale convergence by Nguetseng and Allaire.
Ore 14:30, Aula Picone
Mathematical and numerical modelling of cardiovascular problems has experienced a terrific progress
in the last years, evolving into a unique tool for patient-specific analysis. However, the extensive
introduction of numerical procedures as a part of an established clinical routine and more in
general of a consolidated support to the decision making process of physicians still requires some
steps both in terms of methods and infrastructures (to bring computational tools to the operating
room or to the bedside). The quality of the numerical results needs to be carefully assessed and
certified. An important research line - quite established in other fields - is the integration of
numerical simulations and measurements in what is usually called Data Assimilation. A rigorous
merging of available data (images, measures) and mathematical models is expected to reduce the
uncertainty intrinsic in mathematical models featuring parameters that would require a
patient-specific quantification; and to improve the overall quality of information provided by
measures. However, computational costs of assimilation procedures - and in particular variational
approaches - may be quite high, as typically we need to solve inverse problems, dual and possibly
backward-in-time equations. For this reason, appropriate model reduction techniques are required, to
fit assimilation procedures within the timelines and the size of patient cohorts usually needed by
medical doctors. In this talk, we will consider some applications of variational data assimilation
in vascular and cardiac problems and associated model reduction techniques currently investigated to
bring numerical simulations into the clinical routine. For solving incompressible flows in network
of pipes we will address hierarchical modeling (HiMod) of the solution of partial differential
equations in domains featuring a prevalent mainstream, like arteries. The HiMod approach consists of
approximating the main direction of each vessel with finite elements, coupled with spectral
approximation of the transverse dynamics. The rationale is that a few modes are enough to a reliable
approximation of secondary motion. In addition, modal adaptivity allows to tune the local accuracy
of the model. This results in a "psychologically" 1D modeling to be compared with classical
approaches based on the Euler equations. Finally, we will address some more advanced applications of
geometrical processing for (a) investigating patient-specific bioresorbable stents; (b) supporting
decision making of neurosurgeons in deploying flow diverters for cerebral aneurysms.
Ore 14:30, Aula di Consiglio
Seminario di Algebra e Geometria
Ricorderò i risultati classici di Brenner-Butler, Happel-Ringel e Rickard riguardanti le
equivalenze indotte da moduli tilting finitamente generati (e complessi tilting). Presenterò
la generalizzazione naturale a moduli tilting infinitamente generati, le proprietà delle classi
tilting e le equivalenze indotte. Accennerò ad un recente problema posto da Saorin
riguardante le proprietà della categoria abeliana "cuore" della t-struttura associata a un modulo
tilting.
Ore 16:00, Aula F, Università di Roma III
Colloquium di Matematica
The subject of the talk will be a collection of projective varieties that contain the moduli space
M_g of smooth curves of genus g as a dense open subset. The main focus will be on explaining how
this set of models arises in three apparently rather different contexts: as modular
compactifications (generalizing the Deligne-Mumford compactification by stable curves), as GIT
quotients of pluricanonnical Hilbert schemes, and via the log minimal model program in birational
geometry. I will provide a bit of basic background on each of these threads and then review the
parallel progress in our understanding of them.
Ore 11:00, Aula 34 (quarto piano), Dipartimento di Scienze Statistiche
A two-way live connection involving give-and-take between teaching and research makes me feel very
excited as a teacher every day at the real prospect of becoming more effective in a classroom. I may
add that some of my recent research on statistical inference and related topics has tended to
originate largely from teaching. In turn, such research energizes my role as a teacher. In this
presentation, I will highlight a number of such interesting problems along with their often
unassuming origins. In doing so, I will touch upon Student's t-distributions, multivariate
normality, as well as sufficiency, ancillarity, and Basu's example.
Ore 14:30, Aula 211, Università di Roma III
Seminario di Geometria
We present a number of questions concerning certain 'tautological' cycles on varieties. These
questions have often 'motivic' backgrounds. Links and partial solutions to various conjectures will
be discussed.
Ore 16:00, Aula E
Seminario di Didattica della Matematica
Ore 16:15, Aula di Consiglio
The transport properties of electrons through one dimensional nano devices are today reachable in
experiments and their theoretical modelisation can be achieved using conformal field theory
techniques. I will present a simple model of a scale invariant junction of several quantum wires
described by free massless bosonic fields and construct a non equilibrium stationary state where the
exactly solvable nature of the model allows us to compute the large deviations of the full counting
statistics of energy and charge transport.
Ore 10:00, Aula 34 (quarto piano), Dipartimento di Scienze Statistiche
The talk concerns with the large-time behavior of a class of hyperbolic systems of partial
differential equations and its relation with corresponding (reduced) parabolic equations. The basic
prototype is the Goldstein-Kac model for correlated random walks, interpreted as a variation of the
classical heat equation. Areas of interest of the topic will be presented, together with a selection
of known rigorous mathematical results available in the literature. Additionally, the asymptotic
description of a generalization of the Goldstein-Kac model to an arbitrary number of speeds in
several dimensions (based on an application of a variant of the Kirchoffu2019s matrix tree Theorem
from graph theory) will be presented in details.
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