Notiziario Scientifico
Settimana dal 13 al 19 ottobre 2014
Lunedì 13 ottobre 2014
Martedì 14 ottobre 2014
Martedì 14 ottobre 2014
Martedì 14 ottobre 2014
Martedì 14 ottobre 2014
Mercoledì 15 ottobre 2014
Giovedì 16 ottobre 2014
Giovedì 16 ottobre 2014
Giovedì 16 ottobre 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 14:30, Aula di Consiglio
Seminario di Analisi Matematica
We consider a purely variational approach to time dependent problems, yielding the existence of
global parabolic minimizers. These evolutionary variational solutions are obtained as limits of maps
depending on space and time minimizing certain convex variational functionals. In the simplest
situation, the method provides the existence of global weak solutions to Cauchy-Dirichlet problems
of parabolic systems. This is a joint collaboration with V. Bu0161gelein and F. Duzaar.
Ore 14:00, Aula 5, Edificio Fermi, dipartimento di Fisica
The crossover or Kovacs effect is, roughly speaking, the non-monotonic relaxation of a physical
quantity to equilibrium, from an initial non-equilibrium state in which the considered property had
its equilibrium value. We investigate it in two cases (i) glassy systems, (ii) granular gases. In
the former and with the usual cooling protocol, the time evolution of the energy always passes
through a maximum (normal behavior). Within a very simple model, we discuss the relevance of recent
linear response results for the understanding of this memory effect. The granular gas case is quite
different, since we deal with an intrinsically out-of-equilibrium system due to the continuous loss
of energy in collisions. By introducing a simple energy input mechanism (the so-called stochastic
thermostat), the granular gas reaches an out-of-equilibrium steady state. When looking for memory
effects, we have to substitute relaxation to equilibrium by relaxation to its non-equilibrium steady
state. A simple à la Kovacs protocol for the driving is investigated, for which a crossover effect
is displayed by the granular temperature (kinetic energy). Interestingly, it becomes anomalous for
large enough inelasticity: the granular temperature shows a minimum instead of a maximum. The
underlying physical mechanism for both the normal and anomalous behavior is also discussed, together
with some perspectives for possible future research.
Ore 14:30, Aula 311, Università di Roma II
Seminario di Fisica Matematica
Physical systems typically consist of a large number of interacting particles, which makes
predictions from the time-dependent Schroedinger equation very difficult. Therefore one is
interested in deriving simpler effective evolution equations approximating the Schroedinger
equation. We consider the mean-field limit of fermionic systems and derive Hartree-Fock theory. We
point out a semiclassical structure which is crucial for controlling the approximation up to long
times. If time permits we will discuss recent work extending our results to mixed states, e.g.
systems at positive temperature. (Based on joint work with Marcello Porta, Chiara Saffirio, and
Benjamin Schlein.)
Ore 15:00, Aula di Consiglio
Seminario di Modellistica differenziale numerica
In this talk we consider optimal control problems in which there is an infinite number of ex-ante
identical agents. The evolution of the idiosyncratic state variables follows a controllable ItÙ
process, that is, there exists a vector of controls that allows the planner to modify the individual
state of each agent. In addition there are some aggregate states. In this problem, the aim of the
planner is to maximize an optimality criterion over the full distribution (across agents) of state
variables. The evolution of the state distribution across agents can be characterized by the
Kolmogorov forward (KF) equation In this talk we discuss a particular case of interest: the analysis
of constrained efficiency in heterogeneous agents economies. The constrained efficient allo- cation
is defined as the one of a social planner who maximizes a utilitarian social welfare function (SWF)
subject to the same equilibrium budget con-straints and competitive price setting as the individual
agents. The planner cannot complete markets or use any transfers between agents. We employ the
techniques developed here to compare the solution of this problem with the case of a competitive
equilibrium in which each agent maximizes its own dis- counted utility subject to its state dynamics
taking the aggregate conditions and the dynamics of the other agents as given. Joint work with B.
Moll (Princeton University).
Ore 16:00, Aula D'Antoni, Università di Roma II
Seminario di Analisi Complessa
I will summarize our knowledge of the theory of holomorphic locally homogeneous geometric structures
on compact complex manifolds. In particular, I will discuss Dumitrescùs conjecture that if a
compact complex manifold has c_1=0 and such a structure, then the manifold is a torus and the
structure is translation invariant.
Ore 14:30, Aula di Consiglio
Seminario di Algebra e Geometria
A definite connection is an SO(3)-connection over a 4-manifold, whose curvature is non-zero on every
tangent 2-plane. Such geometric objects were first considered by Allan Weinstein and were called fat
bundles. Given such a connection, the associated S2-bundle is naturally a symplectic manifold.
Surprisingly the symplectic manifold is either a symplectic Fano or a symplectic Calabi-Yau.
Important examples of such connections come from differential geometry. Namely, the Levi-Cevita
connection on the twistor bundle of a Riemannian 4-manifold with sufficiently pinched curvature is
definite. In particular we have examples such as the unit S4 that give rise to positive definite
connections and examples such as hyperbolic 4-manifolds that give rise to negative definite
connections. In this talk I will discuss the following sphere-type theorem: the only four manifolds
that admit an S1-invariant definite connection are S4 and CP2. This work is joined with Joel Fine.
Ore 14:00, Aula di Consiglio
Seminario P(n): Problemi differenziali non lineari
La famosa disuguaglianza di Faber-Krahn afferma che, a parita' di volume, il primo autovalore di
Laplace-Dirichlet e' minimo sulla palla euclidea n-dimensionale. Per operatori completamente non
lineari uniformemente ellittici, se da un lato e' possibile definire l'autovalore principale e
stabilirne alcune proprietà' analoghe a quelle del primo autovalore di Laplace-Dirichlet, d'altro
canto non sono ancora state studiate le sue proprietà' di monotonia rispetto alla simmetria del
dominio. Presenteremo un calcolo esplicito dell'autovalore e dell'autofunzione principale per uno
degli operatori estremali di Pucci in una classe di domini piani, dimostrando come, a parità' di
volume, l'autovalore sia minimo sull'insieme più' simmetrico. I risultati sono stati ottenuti in
collaborazione con I. Birindelli.
Ore 14:30, Aula 211, Università di Roma III
Seminario di Geometria
Let (S,H) be a general primitively polarized K3 surface. I will talk about a joint work with
Concettina Galati, where we prove the existence of curves in the complete linear system |nH| with
A_k singularities and living in families of the "expected dimension". This generalizes results in
the nodal case of Mumford for n=1 and Chen for n > 1. The proof is by degenerating the K3 surface to
a union of rational normal scrolls and deform a higher order tacnode on a curve on the degerated
surface
Ore 16:00, Aula 211, Università di Roma III
Seminario di Probabilità
First we will review a couple geometric invariants of graphs, such as the isoperimetric constant,
hyperbolicity and vertex transitivity. Then we will discuss their manifestation in the behaviour of
the simple random walk on the graph, in particular the existence of non constant bounded harmonic
functions
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.