Notiziario Scientifico
Settimana dal 24 al 30 giugno 2013
Lunedì 24 giugno 2013
Martedì 25 giugno 2013
Martedì 25 giugno 2013
Martedì 25 giugno 2013
Martedì 25 giugno 2013
Martedì 25 giugno 2013
Mercoledì 26 giugno 2013
Mercoledì 26 giugno 2013
Giovedì 27 giugno 2013
Giovedì 27 giugno 2013
Giovedì 27 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
In 1956, Alexandrov proved that any embedded hypersurface in R^n with constant mean curvature is a
round sphere. I will discuss how Alexandrov's theorem can be extended to constant mean curvature
surfaces in certain Riemannian manifolds. This problem turns out to have unexpected links with
general relativity. I will also discuss minimal surfaces in the sphere S^3, and the proof of the
Lawson conjecture.
Ore 12:00, Aula di Consiglio
Seminario di Modellistica differenziale numerica
The term "resource curse phenomenon" refers to countries with an abundance of natural resources,
in particular nonrenewable ones such as minerals or fuels, that tend to have less economic growth
and worst development than other countries with fewer resources. Starting from a work of 2006 we
extended and developed two models, the first nonevolutive and the second a discrete-time one, to
analyze graphically and numerically how resources, population and in particular institutions are
related with market prices. This work is part of my PhD thesis and it is with the advice of Italo
Capuzzo Dolcetta.
Ore 14:30, Aula D'Antoni, Università di Roma II
Seminario di Equazioni Differenziali
In 1926, Hopf showed that every compact, simply connected manifold with constant curvature 1 is
isometric to the standard round sphere. Motivated by this result, Hopf posed the question whether a
compact, simply connected manifold with sufficiently pinched curvatured must be a sphere
topologically. This question has been studied by many authors during the past decades, a milestone
being the topological sphere theorem of Berger and Klingenberg. I will discuss the history of this
problem and sketch the proof of the Differentiable Sphere Theorem (obtained in joint work with
Schoen in 2007). The proof relies on the Ricci flow method pioneered by Richard Hamilton.
Ore 15:00, Aula di Consiglio
Seminario di Modellistica differenziale numerica
In this talk an a-posteriori error analysis for optimal control problems is discussed. In
particular, the error analysis is applied to reduced-order Galerkin approximations for the optimal
control problems. In particular, proper orthogonal decomposition (POD) is utilized to derive
reduced-order approximations. Using the error analysis one can estimate the difference between the
suboptimal (POD) solutions and the associated exact (but unknown) optimal solutions. Numerical
examples illustrate the realization of the error analysis for certain applications.
Ore 16:00, Aula di Consiglio
Seminario di Modellistica differenziale numerica
We provide a framework to study dynamical systems with discontinuous dynamic data, but in which the
state space is structured in a cooperative manner that allows for a complete description of the
trajectories. We offer some examples and results on weak and strong invariance, and suggest possible
future research directions.
Ore 16:15, Aula D'Antoni, Università di Roma II
Seminario di Analisi Complessa
Loewner theory, introduced by Charles Loewner (Karl Loewner) in 1923, provided us one of the most
powerful techniques in the theory of univalent functions. On the other hand, Bers raised
quasiconformal entensions problem of univalent funcions which is motivated by the theory of
universal teichmuller spaces. The purpose of this talk will be to present how Loewner theory
approaches the quasiconformal extension problem. The study also goes to quasiconformality of the
boundary of evolution families of order d.
Ore 14:00, Aula C
Lavoro in collaborazione con N. Gozlan e P-M. Samson. Introdurremo, in uno spazio metrico generico,
una nozione di gradiente che ci permetterà di dare un senso alle soluzione dell'equazione di
Hamilton Jacobi in termine di un operatore d'inf-convoluzione (formula di Hopf-Lax). Daremo due
applicazioni a tale costruzione: 1) Miglioreremo (al caso dei spazi metrici) il famoso risultato di
Otto-Villani sul fatto che la disuguaglianza di log-Sdobolev implica la disuguaglianza di Talagrand;
2) Daremo una caratterizzazione delle disuguaglianze di Poincaré in termine di concentrazione
della misura a-dimensionale.
Ore 14:30, Aula di Consiglio
Seminario di Algebra e Geometria
I will explain how to express the structure ring of the derived self-intersection closed subvariety
X of Y in terms of the universal enveloping algebra of a suitable Lie algebroid. I'll give a few
applications to obstruction theory, and sketch a conjectural dictionary between Lie theory and
algebraic geometry.
Ore 14:30, Aula 311, Università di Roma III
Seminario di Geometria
One defines two ways of constructing rational maps derived from other rational maps, in a
characteristic-free context. The first introduces the Newton complementary dual of a rational map.
One main result is that this dual preserves birationality and gives an involutional map of the
Cremona group to itself that restricts to the monomial Cremona subgroup and preserves de
Jonquières maps. The second construction is an iterative process yielding, in particular,
infinite families of Cohen-Macaulay Cremona maps with prescribed dimension, codimension and degree.
Ore 14:30, Aula 211, Università di Roma III
Seminario di Probabilità
Lavoro in collaborazione con N. Gozlan, P-M. Samson e P. Tetali. Introdurremo una nozione di
cammino, su un grafo, che interpola tra due misure di probabilità. Dimostreremo che tale
interpolazione può soddisfare, in alcuni esempi specifici (grafo completo, ipercubo), una
disuguaglianza di convessità dell'entropia che di conseguenza, come nel caso continuo,
implica una disuguaglianza del tipo log-Sobolev. Tale costruzione è legata ad una nozione di
trasporto ottimale (nel discreto) che introdurremo.
Ore 14:30, Aula di Consiglio
In the late 19th century, mathematicians were interested in problems such as this one: given four
generically placed lines in three dimensions, how many other lines intersect all four? This question
and many others can be formulated in terms of the intersections of subvarieties of the Grassmannian
of k-planes in n-space, or more generally, flag varieties (whose points are sequences of inclusions
of vector spaces). These intersection questions inside the flag variety and some generalizations,
together with related algebraic and combinatorial questions, form the field of Schubert calculus. Of
primary importance is that flag varieties can be realized as algebraic, symplectic manifolds with
Hamiltonian actions by a compact torus. Among the magic properties are that the torus acts with
isolated fixed points, and that codimension-one tori fix only points and two-spheres. The desire to
compute associated algebraic invariants, such as the product structure of associated rings in
special bases, has spawned many combinatorial and graph-theoretic objects. In this talk, we will
discuss some graphs associated to certain manifolds with torus actions, and ask the question of how
combinatorial games involving the graphs can be used to answer geometric questions about the
original manifold and intersections of subvarieties therein.
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invitati a comunicare il proprio indirizzo di posta elettronica a
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