Notiziario Scientifico
Notiziario dei Seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 25 aprile al 1 maggio 2016
Martedì 26 aprile 2016
Ore 9:30, aula G, Università di Roma Tre,
l.go san L. Murialdo 1
Secondo Mini Simposio dell'Associazione Romana di Teoria dei Numeri
09:30 Michel Waldschmidt (Université Pierre et Marie Curie)
Some recent results on Diophantine equations
10:10 Chaohua Jia (Chinese Academy of Science)
Kloosterman sums and shifted character sums with multiplicative coefficients
11:00 Shigeru Kanemitsu (Kinki University, Fukoka)
Limiting values of Lambert series and the secant zeta-function
11:40 Leo Murata (Meijin Gakuin University, Tokyo)
Relations among arithmetical functions, sum of digits functions and paper-folding functions
12:20 Christian Maire (Université Franche-Comte)
Decomposition in infinite extensions of number fields
13:00 Alessandro Languasco (Università di Padova)
Hardy-Littlewood numbers and Bessel's functions
15:00 Alessandro Zaccagnini (Università di Parma)
Prime numbers in short intervals: the Selberg integral and its generalisations
15:40 Christophe Delaunay (Université Franche-Comte)
Atypical averages of root numbers of families of elliptic curves
Martedì 26 aprile 2016
Ore 11:30, aula riunioni (I piano), IAC-CNR, via dei Taurini 19
Seminario di Matematica Applicata
Bruce M. Boghosian (Tufts University)
Fokker-Planck Equations for Wealth Distribution Dynamics
Today there are 62 people in the world who have as much combined wealth as half the human
population. In 2010, that figure was 388, so it has dropped by a factor of more than six
in six years. These figures make clear that wealth distributions are dynamic and that wealth
is concentrating. Understanding how and why this is happening, and what if anything needs to
be done about it is an interdisciplinary problem that will ultimately involve mathematicians,
economists, political scientists, and specialists in ethics, justice, and public policy.
Asset-exchange models are mathematical models of wealth distribution that have received much
attention in recent years. They model an economy by a collection of economic agents, who
exchange wealth in pairwise transactions according to idealized rules. Their evolution may be
described by stochastic differential equations, or by nonlinear and nonlocal Boltzmann equations
[Ispolatov, Krapivsky, Redner, 1997] or Fokker-Planck equations [Boghosian, 2014].
One of the simplest yet most intriguing asset-exchange models, called the Yard-Sale Model, predicts
the unbounded concentration of wealth; indeed, the Gini coefficient, a basic measure of wealth
inequality, has been shown to be a Lyapunov functional of this model [Boghosian, Johnson, Marcq, 2015].
Though this is by itself unrealistic, when an Ornstein-Uhlenbeck model of redistribution is added,
the 'Extended Yard-Sale Model' exhibits stable steady-state behavior that is similar in form to
the famous Pareto distribution. When transactions in the model are biased in favor of the wealthier
party [Boghosian, Devitt-Lee, Johnson, Marcq, Wang, 2016], the model also exhibits a phase transition
known as 'wealth condensation' [Bouchaud, Mezard, 2000], in which a finite fraction of the population's
wealth falls into the hands of the wealthiest agent. It has been argued that this transition
provides a first-principles explanation of the phenomenon of oligarchy, and we shall compare the
model's predictions with actual economic data to demonstrate this.
Martedì 26 aprile 2016
Ore 14:00, aula Dal Passo, Università di Roma Tor Vergata
Seminario di Analisi ed Equazioni Differenziali
Michela Procesi (Università di Roma Tre)
Quasi-periodic solutions with beating effects for the NLS on tori
I will discuss the existence and linear stability of classes of
solutions for the NLS on a torus. I will concentrate on quasi-periodic
solutions which arise from the resonances of the NLS normal form and
exhibit a periodic transfer of the Sobolev norm between Fourier modes.
This is a joint work in progress with E. Haus.
Martedì 26 aprile 2016
Ore 14:30, aula D'Antoni, Università di Roma Tor Vergata
Seminario di Geometria Algebrica
Margarida Melo (Università di Roma Tre)
La formula di degenerazione di Jun Li, I
Martedì 26 aprile 2016
Ore 14:30, aula 311, Università di Roma Tre,
l.go san L. Murialdo 1
Seminario di Fisica Matematica
Marco Falconi (Università di Roma Tre)
Scattering theory for Lindblad-type open systems
In this talk I will discuss the long time asymptotics for open quantum systems of Lindblad-type.
The exemplifying model is the quantum dynamics of a particle scattered off a dynamical target,
the latter occupying a compact region of space. Under suitable assumptions on the interaction,
we are able to prove the existence of wave operators, and asymptotic completeness (in a
suitable sense). Even if the Lindblad operator acts on the trace class ideal, one of the main
ingredients for the proof is a theory of scattering for dissipative operators in Hilbert spaces.
Based on a joint work with J. Faupin, J. Frohlich, and B. Schubnel.
Martedì 26 aprile 2016
Ore 15:00, aula di Consiglio
Seminario di Modellistica Differenziale Numerica
Xavier Dupuis (LUISS Università di Roma Guido Carli)
An iterated projection approach for b-convexity constraints
I will present a numerical method for variational problems under b-convexity constraints,
which generalize convexity constraints and are motivated by the principal-agent problem in
economics. Convexity of such optimization problems requires conditions on b identified by
Figalli, Kim and McCann. For a class of b which satisfy these conditions and are tractable
numerically, we apply an iterated projection approach, namely Dykstra's algorithm, to
projection problems. This is a joint work with Guillaume Carlier (Université Paris-Dauphine)
Martedì 26 aprile 2016
Ore 15:15, aula Dal Passo, Università di Roma Tor Vergata
Seminario di Analisi ed Equazioni Differenziali
Marc Quincampoix (Université de Brest)
On representation formulas for long run averaging optimal control problems
We investigate an optimal control problem where the controller aims
consists in minimizing an averaging cost of Cesaro form. The asymptotic
behavior of the values is a classical problem in ergodic control. To study
the long run averaging we consider Cesaro means when the time horizon
of the Cesaro means converges to infinity. A main result of the paper
says that there is at most one possible accumulation point - in the
uniform convergence topology - when the time horizon of the Cesaro
means converges to infinity. This unique accumulation point is explicitly
described by representation formulas involving probability measures on the
state and control spaces. As a byproduct we obtain the existence of a
limit value in some nonexpansive context. Our approach allows to
generalise several results in ergodic control, and in particular it allows
to cope with cases where the limit value is not constant with respect to
the initial condition.
Martedì 26 aprile 2016
Ore 16:30, aula 211, Università di Roma Tre,
l.go san L. Murialdo 1
Colloquium del Dipartimento di Matematica e Fisica
Michel Waldschmidt (Université Pierre et Marie Curie)
Continued fractions: introduction and applications
Mercoledì 27 aprile 2016
Ore 14:30, aula di Consiglio
Seminario di Algebra e Geometria
Paolo Antonini (SISSA)
Non-integrable Lie algebroids
In this seminar we report on work in progress with Iakovos Androulidakis concerning
the integrability problem of Lie algebroids. In many constructions in non commutative
geometry the passage from a singular space to a C* algebra involves the use of a Lie
groupoid as an intermediate desingularization space.
The infinitesimal datum of a Lie groupoid is a Lie algebroid and they appear independently
for example as: foliations, Poisson manifolds, objects that describe the connections on principal
bundles. However in general is not possible to integrate a Lie algebroid to a Lie groupoid
(in contrast to the theory of Lie algebras). The first part of the talk will be concerned with the
discussion of Lie algebroids: basic definitions, examples, the integration problem, the obstructions
to the integrability of Crainic-Fernandes and the discussion of an important non integrable example
given by Molino. In the last part we will explain our idea of removing the obstructions of a transitive
algebroid, passing to a suitable extension, and discuss generalizations.
In these cases one can still perform some of the basic constructions in index theory and non
commutative geometry.
Mercoledì 27 aprile 2016
Ore 16:00, palazzina RM002, Dipartimento SBAI
Seminario di Geometria
Anna Chiara Lai (Sapienza Università di Roma)
Quasicrystals and trigonometric inequalities
Quasicrystals are relatively dense, discrete sets characterized by the ripetitivity of their
patterns and, at the same time, by the lack of a translational symmetry. Such structures
emerge in medieval Arab art, in the form of aperiodic mosaics, as well as in the molecular
arrangement of some alloys. A quasicristalline state of the matter was first observed by Daniel
Shechtman and for this discovery he was awarded of the Nobel prize in Chemistry in 2011.
In this talk we overview the main properties of quasicrystals and the techniques for their
construction. We shall then focus on a result by Mathei and Meyer, that establishes some
trigonometric inequalities (commonly referred to as Ingham type inequalities in the framework
of non-harmonic analysis) for a class of quasicrystals. We finally present a new result, which
extends such Ingham type inequalities to sets that can be decomposed in the finite union of
translations of a fixed lattice. In the two dimensional case, this class of discrete sets includes
well-known tilings of the plane, such as the honeycomb lattice and all the regular lattices.
This talk is based on a joint work with Vilmos Komornik and Paola Loreti.
Giovedì 28 aprile 2016
Ore 16:00, aula 13 (Macroarea), Università di Roma Tor Vergata
Seminario di Fisica Matematica
Alessandro Giuliani (Università di Roma Tre)
Universality of the Hall conductivity in interacting electron systems on
two-dimensional lattices
In this talk I will present a proof of the universality of the transverse (Hall)
conductivity for general weakly interacting electron systems on two-dimensional
periodic lattices, in the absence of disorder.
More precisely, we consider a lattice fermionic many-body Hamiltonian of the form
H0+V, with H0 a gapped quadratic term, and V
a density-density interaction of strength U. We prove that, if U is small
enough, the Kubo conductivity is independent of U, in particular, it is 2kπ
where k is an integer number.
The theorem applies, among others, to the Hubbard-Haldane model, and to the Hubbard-Hofstadter
model, in which cases we can exhibit choices of the parameters for which the transverse
conductivity is non-zero. The proof is based on fermionic cluster expansion techniques
combined with lattice Ward identities, and on a reconstruction theorem that allows us to
compute the Kubo conductivity as the analytic continuation of its imaginary time counterpart.
Recent progresses on the extension of the theorem uniformly in the gap will be briefly discussed.
Joint work with V. Mastropietro and M. Porta.
Venerdì 29 aprile 2016
Ore 11:00, aula 311, Università di Roma Tre,
l.go san L. Murialdo 1
Seminario di Logica
Mehrnoosh Sadrzadeh (Queen Mary University, London)
Scattering theory for Lindblad-type open systems
Lambek introduced pregroup grammers in 1999, as a simplification of his 1956 syntactic calculus.
From then on, Casadio, Lambek and collaborators applied the setting of pregroup grammars to
formalise grammars of many languages, from English and French, to Polish, Italian and Persian.
In 2007, Lambek and Preller showed that compact 2 categories provide semantics for pregroups.
Later, in a serious of papers starting from 2010, Clark, Coecke and myself, together with students
and postdocs, showed that pregroup grammars, through their compact 2 categorical semantics,
can be used to transfer the grammatical structures of phrases and sentences into linear maps
over vector spaces. We then showed how this capability can be used to solve an open problem in
the field of statistical corpus-based models of natural language: developing grammar-preserving
compositional operators with the desired consequence of building vector semantics for phrases
and sentences. In this talk, I will review the statistical corpus-based models that we work with,
show how they can be made compositional using pregroups, and present experimental results
for linguistic tasks.
Venerdì 29 aprile 2016
Ore 15:00, aula INdAM
Control, Dynamics and PDE's
V. Komornik (Université de Starbourg)
Expansions in non-integer bases and fractal phenomena
Expansions in non-integer bases have many connections to combinatorics, probability, ergodic
theory, measure theory and topology. We present various, somewhat unexpected fractal phenomena
related to such expansions. The talk is based on joint research with P. Erdos, I. Joo, P. Loreti,
A. Petho, M. Pedicini, M. de Vries, A. C. Lai, Derong Kong and Wenxia Li.
Tutte le informazioni relative a questo notiziario devono pervenire
esclusivamente all'indirizzo di posta elettronica
seminari@mat.uniroma1.it
entro le ore 24 del giovedì precedente la settimana interessata.
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