Notiziario Scientifico
Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica G. Castelnuovo
Sapienza Università di Roma
Settimana dal 26 novembre al 2 dicembre 2018
Lunedì 26 novembre 2018
Ore 14:15, aula di Consiglio
seminario di Analisi Matematica
Matthieu Alfaro (Universite' de Montpellier)
Long range dispersion vs. Allee effect
In this talk, we study the balance between long range dispersal kernels and the Allee effect in population dynamics models.
To do so, we first investigate the so called Fujita blow up phenomena in presence nonlocal diffusion. We prove that the
Fujita exponent dramatically depends on the behaviour of the Fourier transform of the diffusion kernel near the origin,
which is linked to the tails of J.
Then, as an application of the result in population dynamics models, we discuss the so called hair trigger effect.
Last, if time permits, we consider the spreading properties (acceleration or not?) of equations with nonlocal diffusion
and Allee effect.
Martedì 27 novembre 2018
Ore 14:30, aula 311 - Pal. C, Dipartimento di Matematica e Fisica, Università di Roma Tre,
largo san Leonardo Murialdo 1
seminario di Fisica Matematica
Dr. N. Benedikter (IST Austria)
Optimal Upper Bound for the Correlation Energy of the Mean-Field Fermi Gas
While Hartree-Fock theory is well established as a fundamental
approximation for interacting fermions, it has been unclear how to
describe corrections due to many-body correlations. I explain how
correlations can be described by an effective quadratic Hamiltonian
obtained by bosonizing collective pair excitations. We then use an
approximate Bogoliubov theory to construct a trial state with
Gell-Mann-Brueckner-type energy. Our result justifies the random phase
approximation in the mean-field scaling regime, for repulsive, regular
interaction potentials.
Martedì 27 novembre 2018
Ore 15:00, aula di Consiglio
seminario di Modellistica Differenziale Numerica
Thierry Goudon (INRIA, Sophia-Antipolis)
A staggered discretization for solving the Euler equations
The mathematical modeling of particulate flows naturally lead to
systems of conservation laws involving constraints on velocity fields.
The numerical treatment of the constrained systems of PDEs might lead
to difficulties: it is not clear that different formulations of the
equations remain equivalent at the discrete level, and a careless
approach might give rise to spurious instabilities, or to
unsatisfactory mass and energy balances. This is reminiscent to the
difficulties that appear in the simulation of Euler equations in low
Mach regimes, when using standard Riemann solvers.
We introduce a new class of schemes for the Euler equations that work
on staggered grids, numerical densities and velocities being stored
in different locations. Moreover, the design of the numerical fluxes
is inspired from the principles of the kinetic schemes. Stability
conditions ensuring the positivity of the discrete density and energy
can be identified, for both first and second order version of the
scheme. The method can be incorporated into a suitable splitting
strategy to handle low Mach simulations.
Mercoledì 28 novembre 2018
Ore 14:00, aula di Consiglio
seminario di Algebra e Geometria
Fabrizio Andreatta (Milano Statale)
p-adic variations of automorphic sheaves
Elliptic modular forms are sections of powers of the Hodge bundle. Starting with the
works of J.P. Serre and N. Katz more than 30 years ago, it was discovered that, given a prime number p,
modular forms live in p-adic families. This phenomenon is the geometric counterpart of the theory fo p-adic
deformations of Galois representations and has become a basic tool in modern Number Theory. I will present
joint work with A. Iovita and V. Pilloni where we construct p-adic families of modular forms as sections of
p-adic powers of the Hodge bundle.
Mercoledì 28 novembre 2018
Ore 14:15, aula 211 - Pal. C, Dipartimento di Matematica e Fisica, Università di Roma Tre,
largo san Leonardo Murialdo 1
seminario di Algebra Commutativa
Dott. Federico Campanini (Universita' degli Studi di Padova)
Weak forms of the Krull Schmidt Theorem
According to the classical Krull-Schmidt Theorem for modules, any
module of finite composition length decomposes as a direct sum of
indecomposable modules in an essentially unique way, that is, unique
up to isomorphism of the indecomposable summands and a permutation of
the summands. In 1975, Warfield proved that every finitely presented
module over a serial ring is a finite direct sum of uniserial modules
and posed a problem, essentially asking whether the Krull-Schmidt
Theorem holds for finite direct sums of uniserial modules. The
negative answer to this question was given by A. Facchini in 1996. He
showed that even though the Krull-Schmidt Theorem does not hold for
serial modules, it is possible to prove a weak version of it. This
phenomenon can be found not only for serial modules, but also for
other classes of modules like cyclically presented modules over a
local ring, kernels of morphisms between indecomposable injective
modules, couniformly presented modules, and more generally, for a
number of classes of modules whose endomorphism ring has at most two
maximal right ideals. In all these example, direct-sum decompositions
are described by two invariants (depending on the specific case).
After a brief discussion about the theme of finite direct-sum
decompositions of modules, we consider weak forms of the Krull-Schmidt
Theorem in additive categories. We provide several examples of
additive categories in which weak forms of the Krull-Schmidt Theorem
hold, showing that the number of invariants needed to describe finite
direct-sum decompositions can be arbitrarily large. Finally, we
explain how to find a general pattern that allow to treat all our
examples at the same time. This talk is based on a joint work with
Alberto Facchini
Giovedì 29 novembre 2018
Ore 14:30, aula 211 - Pal. C, Dipartimento di Matematica e Fisica, Università di Roma Tre,
largo san Leonardo Murialdo 1
seminario di Geometria
Matei Toma (Universite' de Lourraine)
Moduli spaces of semistable sheaves; an alternative construction method
When X is a projective manifold and \omega is a rational ample class, modular compactifications of the
moduli space of stable vector bundles on X have been constructed in Algebraic Geometry by putting
appropriate classes of semistable sheaves at the boundary. These compactifications appear as global
quotients. No similar constructions are known over a general compact Kaehler manifold (X,\omega). In
this talk we present an alternative construction method using "local quotients" which covers the case
when \omega is an arbitrary Kaehler class on a projective manifold X. This is the subject of joint
recent work with Daniel Greb. Essential use is made of the notion introduced by Jarod Alper of a
good moduli space of an algebraic stack. Besides solving a wall-crossing issue appearing in the
context of projective manifolds, this alternative construction method is likely to extend to the
general case of Kaehler manifolds.
Giovedì 29 novembre 2018
Ore 16:00, aula 211 - Pal. C, Dipartimento di Matematica e Fisica, Università di Roma Tre,
largo san Leonardo Murialdo 1
seminario di sistemi dinamici
Hans Daniel Lenz (Universita' di Jena)
Almost periodicity and discrete spectrum for topological dynamical systems
We study dynamical systems (X,G,m) with a compact metric space X, a
locally compact, s -compact, abelian group G and an invariant
probability measure m. We show that such a system has discrete
spectrum if and only if a certain space average over the metric is a
Bohr almost periodic function. In this way, this average over the
metric plays for general dynamical systems a similar role as the
autocorrelation measure plays in the study of aperiodic order for
special dynamical systems based on point sets.
Venerdì 30 novembre 2018
Ore 10:30, aula B
gruppo lavoro su Forma di Wulff in meccanica statistica
Misure di Gibbs
Venerdì 30 novembre 2018
Ore 12:00-14:00, aula di Consiglio
seminario MoMA
Domenico Marinucci
Critical Points, Multiple Testing and Point Source Detection for Cosmological Data
Over the last two decades, Cosmology has experienced a sort of revolution, where a flood of data of
unprecedented accuracy has become available by means of a number of different ground-based and satellite
experiments. A particularly striking example is given by the analysis of Cosmic Microwave Background radiation
(CMB); loosely speaking, CMB can be viewed as a snapshot of the Universe taken at the age of recombination, i.e.
"soon after" the Big Bang: very detailed maps have been produced by the NASA satellite WMAP (2003-2009)
and by the ESA satellite Planck (2013-2018). The analysis of these maps entails a number of extremely interesting
mathematical questions, mostly related to the geometry of spherical random fields. In this talk, we shall be
concerned in particular with issues related to detection of point sources (Galaxies) in CMB Data; we shall discuss
in particular the connection with spherical wavelets, distribution of critical points for spherical random fields,
and multiple testing procedures.
Venerdì 30 novembre 2018
Ore 16:00, aula Picone
seminario per insegnanti (Piano Lauree Scientifiche)
Paolo Maroscia (Sapienza Università di Roma)
Come e perché utilizzare il pensiero pitagorico nell'insegnamento della matematica?
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