Notiziario Scientifico
Settimana dal 10 al 16 giugno 2013
Lunedì 10 giugno 2013
Martedì 11 giugno 2013
Martedì 11 giugno 2013
Martedì 11 giugno 2013
Martedì 11 giugno 2013
Martedì 11 giugno 2013
Martedì 11 giugno 2013
Mercoledì 12 giugno 2013
Mercoledì 12 giugno 2013
Mercoledì 12 giugno 2013
Mercoledì 12 giugno 2013
Giovedì 13 giugno 2013
Tutte le informazioni relative a questo notiziario devono pervenire
all'indirizzo di posta elettronica
seminari@mat.uniroma1.it,
o nella casella della posta di Luigi Orsina, entro le ore 9 del venerdì
precedente la settimana di pubblicazione.
Ore 14:30, Aula di Consiglio
Colloquium di Analisi Matematica
Given a Borel A in R^n of positive measure, one can consider its semisum S=(A+A)/2. It is clear that
S contains A, and it is not difficult to prove that they have the same measure if and only if A is
equal to his convex hull minus a set of measure zero. We now wonder whether this statement is
stable: if the measure of S is close to the one of A, is A close to his convex hull? More in
general, one may consider the semisum of two different sets A and B, in which case our question
corresponds to proving a stability result for the Brunn-Minkowski inequality. When n=1, one can
approximate a set with finite unions of intervals to translate the problem onto Z, and in the
discrete setting this question becomes a well studied problem in additive combinatorics, usually
known as Freiman's Theorem. In this talk I will review some results in the one-dimensional discrete
setting, and show how to answer to this problem in arbitrary dimension.
Ore 14:00, Aula di Consiglio
Seminario di Geometria Algebrica
The theory of p-adic modular forms as created by Serre, Swinnerton-Dyer (and in a more geometric
setting by Katz) should admit a generalization to Siegel modular forms. However, most results need
to be modified suitably; in some cases, completely new methods of proof are needed. I will give a
survey on results obtained in the spirit of Serre's work.
Ore 14:15, Aula D'Antoni, Università di Roma II
Seminario di Equazioni Differenziali
In this talk, I will outline my recent proof of the following statement: An asymptotically flat
3-manifold (M,g) of nonnegative scalar curvature that contains a complete (non compact), properly
embedded stable minimal surface is isometric to the Euclidean space. Since the nonnegativity of the
scalar curvature is implied by the (time-symmetric) Einstein constraint equations, the previous
result naturally applies to initial data sets in General Relativity. The proof of this theorem is
based on a characterization of finite index minimal surfaces, on classical infinitesimal rigidity
results by Fischer-Colbrie and Schoen and on the positive mass theorem by Schoen-Yau. A key
technical step is the improvement of the decay rate of the second fundamental form of such surface:
this follows from a tilt-excess decay lemma at infinity which exploits ideas of Allard-Almgren and
Schoen-Simon. The talk will be aimed at the general mathematical audience, with plenty of references
to other recent results and open problems in the field.
Ore 14:30, Aula 311, Università di Roma III
Seminario di Fisica Matematica
In the first part of this talk we point out that the linear electrodynamics of hot plasmas must be
formulated in a different way compared to ordinary dielectrics or conductors. The difference is due
to the fact that in a hot plasma collisions are so rare that the mean free path of charged particles
are much longer than the typical wavelengths of all modes of plasma electromagnetic oscillations. As
a consequence, the plasma is dispersive both in time and space. In an infinite homogeneos plasma
space dispersion is reflected in the fact that the conductivity tensor depends on the wavevector of
each plane wave considered. Since plane waves, on the other hand, are not eigenmodes of real,
non-uniform plasmas, space dispersion makes it very difficult to solve the linearized Vlasov
equation to obtain the constitutive relation, i.e. the linear relation between high frequency
current and field in the plasma. In magnetically confined plasmas the particle orbits are
multi-periodic. This has suggested (Kaufmann 1972) the use of action-angle variables to solve the
problem. This approach is fascinatingly simple and elegant, but the results, if taken literally,
lead to predictions which contraddict expectation and experimental evidence. Investigating the
reason of these paradoxes is very interesting, since it is a first step to understand how
irreversibility arises from a reversible model, and to the construction of a consistent 'closed'
theory of linear wave propagation in plasmas. In the second part of the talk we sketch the solution
of the linearized Vlasov equation with the spectral method. The integral, non local constitutive
relation obtained in this way is very complicated, but physically transparent, and is, therefore, a
good starting point for approximations based on clearly formulated assumptions, which lead to wave
equations valid for concrete problems, and which can be numerically solved with a reasonable effort.
To confirm this, we will finally show a few pictures of wave propagation in tokamaks in the Ion
Cyclotron range of frequencies, obtained with the full-wave solver TORIC.
Ore 14:30, Aula 211, Università di Roma III
Seminario di Geometria
A vector bundle E on a variety X embedded in a n-dimensional projective space is Ulrich if for some
linear projections X in P^[n-1] the direct image of E is trivial. The existence of an Ulrich bundle
on a k-dimensional variety X implies that the cone of cohomology tables is the same as for the
k-dimensional projective space. It is expected that every projective variety admits an Ulrich
bundle. We will discuss how Lazarsfeld-Mukai bundles on K3 surfaces provide examples of rank 2
stable Ulrich bundles. Our results imply, by using the work of Eisenbud and Schreyer, that the Chow
form of a polarized K3 surface admits a pfaffian Bezout form in Plucker coordinates. This is a joint
work with Gavril Farkas and Marian Aprodu.
Ore 15:15, Aula D'Antoni, Università di Roma II
Seminario di Equazioni Differenziali
We prove some old and new isoperimetric inequalities with the best constant via the ABP method. More
precisely, we obtain a new family of sharp isoperimetric inequalities with weights (or densities) in
open convex cones of R^n. Our results apply to all nonnegative homogeneous weights satisfying a
concavity condition in the cone. Surprisingly, even that our weights are not radially symmetric,
Euclidean balls centered at the origin (intersected with the cone) minimize the weighted
isoperimetric quotient. As a particular case of our results, we provide with new proofs of classical
results such as the Wulff inequality and the isoperimetric inequality in convex cones of Lions and
Pacella. Furthermore, we also study the anisotropic isoperimetric problem for the same class of
weights and we prove that the Wulff shape always minimizes the anisotropic weighted perimeter under
the weighted volume constraint.
Ore 16:15, Aula D'Antoni, Università di Roma II
Seminario di Analisi Complessa
This talk will be about a family of operads that act on spaces of knots and what they have to say
about the homotopy-type of embedding spaces. In the 3-dimensional case this operad "sees"
geometrization. In high dimensions its still unclear to what extent this operad offers insight.
Ore 14:30, Aula di Consiglio
Seminario di Algebra e Geometria
Stratified spaces are a common and general class of singular spaces, including orbit spaces and
algebraic varieties. Their homology does not satisfy Poincaré duality, but their
"intersection homology" satisfies a generalized Poincaré duality. On certain stratified
spaces, "Witt spaces", this topological theory due to Goresky-MacPherson is dual to the analytic
L^2-cohomology of Cheeger. I will report on joint work with Eric Leichtnam, Rafe Mazzeo, and Paolo
Piazza, in which we have constructed extensions and refinements of these theories to general
stratified spaces.
Ore 14:30, Aula 1B1, Dipartimento SBAI
I will first describe the basic ideas concerning fractional Laplacians, as well as the essential
tools to treat nonlinear equations involving these operators. I will then present recent results on
fractional semilinear elliptic equations (mainly of Allen-Cahn type) and on front propagation for
fractional Fisher-KPP type equations.
Ore 15:00, Aula G
Seminario di Geometria
Si definisce la nozione di (s,t)-fibrazione, ovvero fibrazione generalizzata in uno spazio
proiettivo PG(d,q) e si dimostrano alcune proprietà della fibrazione stessa.
Ore 16:00, Aula Dal Passo, Università di Roma II
There have been several attempts to generalize the notion of tracial ultrapower of II_1 factors to
general von Neumann algebras. However, no connection among those approaches have been known. In this
talk, I will introduce three central sequence algebras (Connes,Golodets,Ocneanu)/three ultraproducts
(Golodets,Ocneanu,Groh-Raynaud) and show that they can be treated in a unified way. Using the
connection among them, some spectral properties of the modular operator of the ultrapower state on
the Ocneanu ultrapower of type III factors are presented. Also, I also present the quesitons/answers
whether ultrapower of factors are factors or not. This is a joint work with Uffe Haagerup.
Ore 11:00, Aula di Consiglio
Seminario P(n): Problemi differenziali non lineari
We establish a lower bound for the number of sign changing solutions with precisely two nodal
domains to the singularly perturbed nonlinear elliptic equation -L^2Delta _[g]u+u=|u|^[p-2]u on an
n-dimensional Riemannian manifold M, p in (2,2^*), in terms of the cup-length of the configuration
space of M. We give a precise description of the asymptotic profile of these solutions as L tends to
0. We also provide new estimates for the cup-length of the configuration space of M. This is joint
work with Anna Maria Micheletti.
Tutti coloro che desiderano ricevere questo notiziario via e-mail sono
invitati a comunicare il proprio indirizzo di posta elettronica a
seminari@mat.uniroma1.it.
Il Direttore
Il calendario dei seminari è anche
disponibile su
internet.