Notiziario Scientifico
Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica G. Castelnuovo
Sapienza Università di Roma
Settimana dal 5 novembre all'11 novembre 2018
Lunedì 5 novembre 2018
Ore 14:15, aula di Consiglio
seminario di Analisi Matematica
Lucio Boccardo
Rileggendo la mia tesi di laurea: nuovi risultati sulla stabilità
dei minimi di funzionali del Calcolo delle Variazioni
Lunedì 5 novembre 2018
Ore 14:50, aula di Consiglio
seminario di Analisi Matematica
Italo Capuzzo Dolcetta
A short presentation of some results on the weak maximum principle
Lunedì 5 novembre 2018
Ore 14:30, aula Dal Passo, dipartimento di Matematica,
Università di Roma Tor Vergata, via della Ricerca Scientifica 1
seminario
Paolo Bravi (Università di Roma "La Sapienza")
Spherical functions and orthogonal polynomials
I will explain how some questions we asked a few years ago on the multiplication of spherical
functions on symmetric spaces are related to the so-called linearization problem for a certain
kind of orthogonal polynomials, namely Jacobi polynomials. I will state some conjectures in the
particular case of Jack polynomials.
Lunedì 5 novembre 2018
Ore 16:00, aula Dal Passo, dipartimento di Matematica,
Università di Roma Tor Vergata, via della Ricerca Scientifica 1
seminario
Niels Kowalzig (Università di Napoli "Federico II")
Higher brackets on cyclic and negative cyclic (co)homology
In this talk, we will embed the string topology bracket developed by Chas-Sullivan and Menichi
on negative cyclic cohomology groups as well as the dual bracket found by de Thanhoffer de Voelcsey-Van
den Bergh on negative cyclic homology groups into the global picture of a noncommutative differential
(or Cartan) calculus up to homotopy on the (co)cyclic bicomplex in general, in case a certain Poincaré
duality is given. For negative cyclic cohomology, this in particular leads to a Batalin-Vilkovisky algebra
structure on the underlying Hochschild cohomology. In the special case in which this BV bracket vanishes,
one obtains an e_3-algebra structure on Hochschild cohomology. The results are given in the general and
unifying setting of (opposite) cyclic modules over (cyclic) operads. All this is joint work with D. Fiorenza.
Martedì 6 novembre 2018
Ore 15:00, aula di Consiglio
seminario di Modellistica Differenziale Numerica
Claudio Estatico (Università degli Studi di Genova)
Regularization methods in variable exponent Lebesgue spaces
Let us consider a functional equation Ax=y characterized by an ill-posed
linear operator A acting between two Banach spaces X and Y. In this talk,
we propose an extension of the Tikhonov regularization approach to the (unconventional)
setting where X and Y are both two variable exponent Lebesgue spaces. Basically,
a variable exponent Lebesgue space is a (non-Hilbertian) Banach space where the exponent
used in the definition of the norm is not constant, but rather is a function of the domain.
This way, we can automatically assign different "amount" of regularization, related
to different values of the exponent function, on different regions of the domain.
In the case of image deblurring problems, different pointwise regularization is useful
because background, low intensity, and high intensity values of the image to restore require
different filtering (i.e., regularization) levels, depending on the local signal to noise
ratios in all the different portions of the image domain. A numerical evidence will be also
discussed.
References
Diening, L., Harjulehto, P., Hästö, P., Ruzicka, M., Lebesgue and Sobolev spaces with variable exponents. Lecture Notes in Mathematics. vol. 2017, Springer, 2011.
Schuster, T., Kaltenbacher, B., Hofmann, B., and Kazimierski, K. S., Regularization Methods in Banach Spaces. Radon Series on Computational and Applied Mathematics, vol. 10, De Gruyter, 2012
C. Estatico, S. Gratton, F. Lenti, D. Titley-Peloquin, A conjugate gradient like method for p-norm minimization in functional spaces, Numerische Mathematik,
Martedì 6 novembre 2018
Ore 16:00, aula D'Antoni, dipartimento di Matematica,
Università di Roma Tor Vergata, via della Ricerca Scientifica 1
seminario di Analisi Complessa
Tatsuo Suwa (Hokkaido University)
Relative Dolbeault cohomology and its application to the Sato hyperfunction theory
The Cech-de Rham cohomology together with its integration theory has been effectively used in
various problems related to localization of characteristic classes. Likewise we may develop
the Cech-Dolbeault cohomology theory and on the way we naturally come up with the relative
Dolbeault cohomology. This cohomology turns out to be canonically isomorphic with the local
(relative) cohomology of A. Grothendieck and M. Sato so that it provides a handy way of
representing the latter. In this talk we present the theory of relative Dolbeault cohomology
and give, as applications, simple explicit expressions of Sato hyperfunctions, some fundamental
operations on them and related local duality theorems. Particularly noteworthy is that the
integration of hyperfunctions in our framework, which is a descendant of the integration
theory on the Cech-de Rham cohomology, is simply given as the usual integration of Stokes
type. Also the Thom class in relative de Rham cohomology plays an essential role in the
scene of interaction between topology and analysis. The talk includes a joint work with N. Honda and T. Izawa.
Mercoledì 7 novembre 2018
Ore 11:00, aula B
Gruppo lavoro su "Forma di Wulff in meccanica statistica"
Lorenzo Bertini
Breve introduzione alla meccanica statistica, modello di Ising e corrispondente transizione di fase.
Mercoledì 7 novembre 2018
Ore 14:00, aula di Consiglio
seminario di Algebra e Geometria
Benoît Cadorel (IMT)
Subvarieties of quotients of bounded symmetric domains
The main conjecture of the field of complex hyperbolicity, due to Green, Griffiths and Lang,
states that a complex projective manifold of general type should contain a proper algebraic
"exceptional" locus, containing all the entire curves, and all the subvarieties
which are not of general type.
This problem has recently attracted a lot of attention for manifolds which are compactifications
of quotients of bounded symmetric domains by arithmetic lattices. Recent results of Brunebarbe and
Rousseau show that such a variety satisfies the Green-Griffiths-Lang conjecture, provided the
lattice is small enough. Our goal is to present a approach based on a metric positivity criterion
of Boucksom, which allows to state precise conditions for the subvarieties to be of general type,
or for the entire curves to be included in the boundary. If we assume the Green-Griffiths-Lang
conjecture, our criteria permit in principle to get upper bounds for the dimension of the exceptional
locus, independently of the choice of lattice: we will illustrate this by giving new effective examples
for quotients of the ball, or of the generalized upper half space of Siegel.
Giovedì 8 novembre 2018
Ore 14:30, aula di Consiglio
seminario P(n)/N(p)
Zhang Jianjun (Department of Science and High Technology and RISM - Riemann International School of Mathematics,
Università degli Studi dell'Insubria)
On weakly coupled elliptic systems with critical growth
In this talk, we are concerned with positive vector solutions of Bose-Einstein
type systems in dimension four and two. The interaction is critical in the sense
of Sobolev in dimension four and of critical exponential type in the sense of
Moser in dimension two. In dimension four, via the Hopf fibration approach,
concentration phenomena around spheres are investigated in the attractive case
as the Planck constant goes to zero. As for dimension two, we prove, using
variational methods, the existence of positive vector ground state solutions
both in the attractive and repulsive cases. This talk is based on joint work
with Jo~ao Marcos do O and with Daniele Cassani and Hugo Tavares
Venerdì 9 novembre 2018
Ore 14:00, Aula 8, Università UNINT, Via C. Colombo 200
seminario
Maria Artale (Università di Roma Tor Vergata)
Moduli di Weyl e ordine di Bruhat
Venerdì 9 novembre 2018
Ore 16:00, aula Picone
seminario per insegnanti (Piano Lauree Scientifiche)
Claudio Bernardi (Sapienza Università di Roma),
Antonio Fanelli (Liceo Plinio Seniore),
Giuliana Massotti (Liceo Avogadro),
Antonio Veredice (Liceo Peano di Monterotondo)
Che cosa proporre di logica nel Liceo Matematico?
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