Notiziario Scientifico
Settimana dal 19 al 25 maggio 2014
Lunedì 19 maggio 2014
Lunedì 19 maggio 2014
Martedì 20 maggio 2014
Martedì 20 maggio 2014
Martedì 20 maggio 2014
Martedì 20 maggio 2014
Mercoledì 21 maggio 2014
Mercoledì 21 maggio 2014
Mercoledì 21 maggio 2014
Mercoledì 21 maggio 2014
Mercoledì 21 maggio 2014
Giovedì 22 maggio 2014
Giovedì 22 maggio 2014
Giovedì 22 maggio 2014
Venerdì 23 maggio 2014
Venerdì 23 maggio 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 14:15, Aula 311, Università di Roma III
Seminario di Algebra Commutativa
Ore 14:30, Aula di Consiglio
Seminario di Analisi Matematica
Ore 14:00, Aula D'Antoni, Università di Roma II
Dynamical Systems working seminars
We introduce the notion of a quasistatic dynamical system (QDS), inspired by the namesake processes
in thermodynamics. The latter are idealized processes in which the observed system transforms
(infinitesimally) slowly due to external influence, tracing out a continuous path of thermodynamic
equilibria over an (infinitely) long time span. We then prove limit theorems for a paradigmatic QDS
consisting of strongly chaotic expanding circle maps. (This is joint work with Neil Dobbs.)
Ore 14:30, Aula 34 (quarto piano), Dipartimento di Scienze Statistiche
Information about social entities in spread across multiple databases, which often do not share
unique identifiers. This information must be assembled in some way. One such way is record linkage,
which does just this. We approach this problem as one of discovering a latent bipartite network,
which links manifest records to a common set of unique individuals. This novel representation lets
use a hierarchical Bayesian model to simultaneously infer the linkage structure, attributes and the
number the latent individuals in the population. This Bayesian method quantifies the uncertainty in
the inference and allows us to propagate the uncertainty into later substantive analyses. We test
our model using data from the National Long Term Care Survey (NLTCS), a longitudinal study of the
health of elderly (65+) individuals (http://www.nltcs.aas.duke.edu). The NLTCS was conducted
approximately every six years, with each wave containing roughly 20,000 individuals. Two aspects of
the NLTCS make it suitable for our purposes: individuals were tracked from wave to wave with unique
identifiers, but at each wave, many patients had died (or otherwise left the study) and were
replaced by newly-eligible patients. We can test the ability of our model to link records across
files by seeing how well it is able to track individuals across waves, and compare its estimates to
the ground truth provided by the unique identifiers. Furthermore, we touch on new work using an
empirical Bayesian model, which has been tested on simulated data and shows improved results for
non-English names.
Ore 15:45, Aula Dal Passo, Università di Roma II
Seminario di Analisi Reale ed Armonica
We look for lower L^[2] bounds for the s-dimensional Riesz transform acting on very general measures
with support on Cantor sets in R^d, for sin(d-1,d). The bounds obtained are written in terms of the
densities of the cubes appearing in the construction of the Cantor sets. Our estimates allow us to
establish an equivalence between the capacity gamma_[s] associated with the s-dimensional Riesz
kernel and the capacity dot[C]_[frac[2][3](d-s),frac[3][2]] from non-linear potential theory related
to the Wolff potential. This is joint work with Xavier Tolsa (Universitat Autonoma de Barcelona).
Ore 16:00, Aula D'Antoni, Università di Roma II
Seminario di Analisi Complessa
Si descrive una costruzione geometrica che produce mappe di tipo gradiente mediante estensione
analitica di opportune rappresentazioni di spazi vettoriali reali nei campi vettoriali di una
sottovarietà reale di una varietà complessa. Nel caso scalare tale costruzione
fornisce in modo naturale equazioni di ipersuperfici reali Levi non degeneri che sono soluzioni
dell'equazione scalare di Monge-Ampère (dd^cu)^n = 0.
Ore 14:30, Aula di Consiglio
Seminario di Algebra e Geometria
The weak order is a nice combinatorial tool intimately related to the study of reduced words in
Coxeter groups. In finite Coxeter groups, it is a lattice and an orientation of the 1-skeleton of
the permutahedron that provides a nice framework to construct generalized associahedra (via N.
Reading's Cambrian lattices). In this talk, we will discuss a conjecture of Matthew Dyer that
proposes a generalization of the framework weak order/reduced words to infinite Coxeter groups. On
the way, we will talk of the relationships between limits of roots and tilings of their convex hull,
imaginary cones, biclosed sets and inversion sets of reduced infinite words (partially based on
joint works with M. Dyer, J.P. Labbé and V. Ripoll).
Ore 14:30, Aula 311, Università di Roma III
Seminario di Analisi e Sistemi Dinamici
I will present an abstract Implicit Function Theorem with parameters for smooth operators defined on
sequence scales of Hilbert spaces, modeled for the search of quasi-periodic solutions for PDEs. As
an application, I will deduce the existence of quasi-periodic solutions for forced NLW and NLS
equations on any compact manifold which is homogeneous with respect to a compact Lie group. (Joint
work with M. Berti and M. Procesi)
Ore 14:30, Aula dei seminari di Fisica, Dipartimento SBAI
Ore 16:00, Aula di Consiglio
Seminario di Fisica Matematica
If the first mathematical results were obtained more than 30 years ago with the interpretation of
the celebrated Hofstadter butterfly, more recent experiments in Bose-Einstein theory suggest new
questions. I will start with a partial survey on old results (Helffer-Sj"ostrand,
Avila-Jitomirskaya-Krikorian,...) and then discuss more recent questions with generalized
butterflies (Dalibard and coauthors, Hou, Kerdelhué-Royo-Letelier). These new questions are strongly
related to the Harper on triangular or hexagonal lattices (in connexion with the now very popular
graphene). Our historics is focused on the mathematical results.
Ore 16:00, Aula 311, Università di Roma III
Seminario di Analisi e Sistemi Dinamici
In my talk I will discuss a recent result obtained with M.Berti and P. Baldi about the existence of
quasi-periodic solutions for Hamiltonian quasi-linear autonomous perturbations of KdV equation. The
proof is based on a Nash-Moser scheme with approximate inverse. The core of the work is the
construction of the approximate inverse for the linearized operator. To do this we apply a recent
method developed by M.Berti and P. Bolle which decouples the dynamic on the action-angle variables
from the dynamic on the normal variables. By means of this method we are reduced to invert a third
order non constant coefficients partial differential operator on the normal directions, to which we
apply a reduction procedure that allows to reduce it to constant coefficients.
Ore 11:00, Aula 1B1, Dipartimento SBAI
Seminario di Geometria
The celebrated nodal domain theorem by Courant says that the number of nodal domains of an
eigenfunction associated with a k-th eigenvalue of the Dirichlet Laplacian (eigenvalues listed in
increasing order) should be less than or equal to k. Pleijel proved in 1956 that equality holds only
for finitely many values of k. In this case we speak of the Courant sharp situation (this has a
strong connection with the question of minimal spectral partitions). If we look at the square, it is
immediate that the first, second and fourth eigenvalues are Courant sharp. We would like to analyze
the statement by Pleijel that there are no other cases. We also discuss some statements of Antonie
Stern who was a PhD student of R. Courant and defended her PhD in 1924. Although we focus on her
results concerning the square, let us mention that she also has similar results in the case of the
sphere, fifty years before the paper of H. Lewy.
Ore 14:00, Aula di Consiglio
Seminario P(n): Problemi differenziali non lineari
Si presentano alcune proprietà analitiche e geometriche delle metriche di Finsler, e qualche
applicazione alla Relatività Generale
Ore 14:30, Aula 34 (quarto piano), Dipartimento di Scienze Statistiche
Much is now known about the consistency of Bayesian updating on infinite-dimensional parameter
spaces with independent or Markovian data. Necessary conditions for consistency include the prior
putting enough weight on the correct neighborhoods of the data-generating distribution; various
sufficient conditions further restrict the prior in ways analogous to capacity control in
frequentist nonparametrics. The asymptotics of Bayesian updating with mis-specified models or
priors, or non-Markovian data, are far less well explored. Here I establish sufficient conditions
for posterior convergence when all hypotheses are wrong, and the data have complex dependencies. The
main dynamical assumption is the asymptotic equipartition (Shannon-McMillan-Breiman) property of
information theory. This, along with Egorovu2019s Theorem on uniform convergence, lets me build a
sieve-like structure for the prior. The main statistical assumption, also a form of capacity
control, concerns the compatibility of the prior and the data-generating process, controlling the
fluctuations in the log-likelihood when averaged over the sieve-like sets. In addition to posterior
convergence, I derive a kind of large deviations principle for the posterior measure, extending in
some cases to rates of convergence, and discuss the advantages of predicting using a combination of
models known to be wrong. An appendix sketches connections between these results and the replicator
dynamics of evolutionary theory.
Ore 11:00, Aula 311, Università di Roma III
Seminario di Logica e Informatica Teorica
In the study of families of dynamical systems depending on a parameter, one interesting issue is the
identification of "bifurcation parameters", that is values for the parameter at which the
dynamical properties of the system change. We are interested in the sets of bifurcation parameters
for the quadratic family and the alfa-continued fractions transformations. It turns out that these
sets are unexpectedly strongly connected, and using this connection some interesting properties for
the two sets are easily derived. Finally we show some applications to seemingly unrelated problems.
This is joint work with C.Carminati, S.Isola and G.Tiozzo.
Ore 15:30, Aula 1B1, Dipartimento SBAI
Seminario di Analisi
Presentero' la teoria di De Giorgi-Nash-Moser estesa ad operatori integro-differenziali non locali.
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