Notiziario Scientifico
Settimana dal 12 al 18 maggio 2014
Lunedì 12 maggio 2014
Lunedì 12 maggio 2014
Lunedì 12 maggio 2014
Lunedì 12 maggio 2014
Martedì 13 maggio 2014
Martedì 13 maggio 2014
Martedì 13 maggio 2014
Martedì 13 maggio 2014
Mercoledì 14 maggio 2014
Mercoledì 14 maggio 2014
Mercoledì 14 maggio 2014
Giovedì 15 maggio 2014
Venerdì 16 maggio 2014
Venerdì 16 maggio 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 14:00, Aula D'Antoni, Università di Roma II
We consider a natural extension of Newton's equations of the N-body problem to spaces of constant
curvature. We first present some qualitative results regarding the motion of the bodies, focusing on
relative equilibria and rotopulsators, which generalize the notion of homographic orbits from
Euclidean to curved space. Then we write the equations in intrinsic coordinates and discuss the
advantages and disadvantages of this approach. Finally we come up with a new and simple form of the
equations that brings together the Euclidean case (of Gaussian curvature k=0), the hyperbolic case
(of Gaussian curvature k < 0), and the elliptic case (of Gaussian curvature k > 0). Thus Newton's
classical equations can be regarded in a broader context, namely that in which the motion of the
bodies takes place in spaces of constant curvature. The equations of motion depend on the curvature
k, and the Euclidean case is recovered when k=0. This conclusion could not be drawn from previously
known forms of the equations of motion in curved space since taking k- > 0, for both k > 0 and k <
0, led to undetermined limits. This new form of the equations of motion allows the study of the
classical case, k=0, in a larger framework and will help us better understand Newton's original
approach.
Ore 14:00, Aula 311, Università di Roma III
Seminario di Algebra Commutativa
Ore 14:30, Aula di Consiglio
Seminario di Analisi Matematica
We will describe recent results on the doubly parabolic Keller-Segel system in the plane, when the
initial data belong to critical scaling-invariant Lebesgue spaces. We analyze the global existence
of integral solutions, their optimal time decay, uniqueness and positivity, together with the
uniqueness of self-similar solutions. We are then able to study the large time behavior of global
solutions and prove that in the absence of the degradation term the solutions behave like
self-similar solutions, while in presence of the degradation term global solutions behave like the
heat kernel.
Ore 15:30, aula XII, Dipartimento di Scienze Statistiche
Corso di Dottorato
Ore 14:00, Aula B
Corso di Dottorato
In this course we will develop the theory of pseudodifferential operators on Euclidean and curved
geometries. We will use these operators to construct refined parametrices and inverses of natural
differential operators. For example given a Riemannian manifold, the resolvent of the Laplacian, the
solution to the wave equation and the solution of the heat equation are all best understood using
the techniques of microlocal analysis. Topics will include: pseudodifferential operators on R^n,
wave front set and pseudolocality, pseudodifferential operators on manifolds, the resolvent of the
Laplacian, elliptic regularity, de Rham cohomology and Hodge theory, Further topics depending on
student interest: Wave equation, Dirac operators, heat equation, Atiyah-Singer index theory, Kahler
package, analysis on non-compact and singular spaces.
Ore 14:30, Aula Zorzi, ex-Mattatoio, Università di Roma III
Seminari Formulas
L'idea rinascimentale della città ideale, realizzata con una forma geometrica, è stata
vista come la dtruttura che meglio ha saputo interpretare l'ideale rinascimentale della città
comunale. Insieme alle due "sorelle", la città-fortezza e la città-utopia, la
città ideale ha impresso sul territorio un marchio duplice, da un lato ha rappresentato la
presenza militare di stati quasi pernennemente in guerra, dall'altro la capacità tecnica di
trasformare in oggetti fisici le analisi teoriche della geometria dell'epoca. Queste città si
prestano ad essere la base per uno studio geometrico e topologico della loro organizzazione,
utilizzando gli strumenti della space syntax e della teoria dei grafi. Le teorie morfologiche
classiche (ad esempio quelle di Conzen e Caniggia) possono essere descritte in termini di teoria dei
grafi utilizzando un procedimento di contrazione degli spazi omogenei e urbanisticamente isomorfi.
L'analisi permette di confrontare le strutture delle differenti città ideali e di misurarne
le proprietà urbanistiche.
Ore 14:30, Aula Dal Passo, Università di Roma II
Seminario di Equazioni Differenziali
The eigenvalue problem of the p-Laplace operator is extensively studied for p > 1. We are interested
in the highly degenerated limit case p=1 where some new phenomena can be observed. First, the formal
eigenvalue equation is not well defined and one has to clarify what an eigensolution of the
1-Laplace operator should be. Then the existence of a sequence of eigensolutions can be shown. Since
the corresponding eigenvalue equation has too many solutions, a further equation satisfied by
eigensolutions is derived.
Ore 16:00, Aula D'Antoni, Università di Roma II
Seminario di Analisi Complessa
Sia X una varietà di Kaehler compatta e D un divisore in X. Studiamo le equazioni di
Monge-Ampere complesse sulla varietà quasi-proiettiva XD e stabiliamo stime a priori uniformi
che generalizzano sia le stime di Yau che quelle di Kolodziej. In particolare, data una
densità f liscia solo su XD, mostriamo che l'unica soluzione dell'equazione di Monge-Ampere
con densità f è anch'essa liscia su XD. I risultati presentati sono stati ottenuti in
collaborazione con Hoang-Chinh Lu.
Ore 14:30, Aula di Consiglio
Seminario di Algebra e Geometria
This is joint work with Mingmin Shen. I will introduce the notion of multiplicative Chow--Kunneth
decomposition and give first examples of varieties endowed with such a decomposition. I will then
explain why we expect hyperkahler varieties to be endowed with such a decomposition, sketch a proof
that the Hilbert scheme of length-2 subschemes on a K3 surface is endowed with such a decomposition
and relate this to the Fourier decomposition.
Ore 15:00, Aula 311, Università di Roma III
Seminario di Analisi e Sistemi Dinamici
We consider the discounted equation lambda u_[lambda](x) + H(x,d_x u_[lambda])=c set on a compact
and connected Riemannian manifold M, where lambda is a positive parameter, H is a continuous
Hamiltonian, coercive in the momentum, and c is the associated critical value. Under these
assumptions, the corresponding solutions u_[lambda]: Mtomathbb R are equi--bounded and
equi--Lipschitz, hence they uniformly converge, along subsequences as the discount factor lambda
goes to 0, to a viscosity solution of the critical equation H(x,d_x u)=c. Due to the lack of a
comparison principle for this latter equation, it is not clear at this point that the solutions
selected at the limit along different subsequences are the same. When H is additionally assumed
convex in the momentum, we prove that the u_[lambda] uniformly converge to a specific solution of
the critical equation, characterized in terms of a class of probability measures introduced in the
framework of weak KAM Theory. This is a joint work with A. Fathi, R. Iturriaga and M. Zavidovique.
Ore 15:45, Aula di Consiglio
Seminario di Algebra e Geometria
This is joint work with Charles Vial. I will explain how to define a Fourier transform using a
conjecturally canonical codimension-2 cycle on the self product of certain hyperkahler fourfolds.
Under certain conditions, the Fourier transform induces a decomposition of the Chow ring. I will
explain how this can be carried out for the variety of lines on a cubic fourfold and the Hilbert
scheme of two points on a K3 surface.
Ore 14:00, Aula di Consiglio
Seminario P(n): Problemi differenziali non lineari
In this talk I will discuss some recent results concerning the existence and uniqueness of large
solutions for singular elliptic and parabolic problems. In the elliptic case a general condition on
the absorption term of the 1-Laplace elliptic equation is given in order to get both existence and
uniqueness. This condition can be considered as the correspondent Keller-Osserman condition for the
p-Laplacian in the case p = 1. In the framework of parabolic p-Laplace equations we will show how
existence and uniqueness of suitable large solutions can be obtained for singular problems (i.e. 1 <
= p < 2) without the presence of lower order absorption terms. All these results have been obtained
in collaboration with Salvador Moll (Universitat de Valencia).
Ore 11:00, Aula 311, Università di Roma III
Seminario di Logica Matematica
One of the strongest trend in computer science is the (relatively recent) interest in exploiting new
computing paradigms which go beyond the usual, classical one. Among these paradigms, quantum
computing plays an important role. In the first part of the talk, we introduce some basic notions
about quantum computing. In the second part, we explain the state of art of (functional) quantum
languages, focusing on the crucial role played by Linear Logic and on the so called "quantum
data+classical" control approach to computation. Finally, we briefly show how Geometry of
Interaction represents a promising tool in order to address the challenging problem of the
definition of (good) semantics for functional calculi.
Ore 15:00, Aula INdAM
This is a joint work with Pierre Pageault. For a homeomorphism h of a compact space, a Lyapunov
function is a real valued function that is non-increasing along orbits for h. By looking at simple
dynamical systems(=homeomorphisms) on the circle, we will see that there are systems which are
topologically conjugate and have Lyapunov functions with various regularity. This will lead us to
define barriers analogous to the well known Peierls barrier or to the Mañé potentialin Lagrangian
systems. That will produce by analogy to Mather's theory of Lagrangian Systems an Aubry set which is
the generalized recurrence set introduced in the 60's by Joe Auslander (via transfinite induction)
and a Mañé set which is essentially Conley's chain recurrent set. No serious knowledge of Dynamical
Systems is necessary to follow the lecture.
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.