Notiziario Scientifico
Settimana dal 19 al 25 gennaio 2015
Lunedì 19 gennaio 2015
Lunedì 19 gennaio 2015
Martedì 20 gennaio 2015
Martedì 20 gennaio 2015
Martedì 20 gennaio 2015
Mercoledì 21 gennaio 2015
Mercoledì 21 gennaio 2015
Mercoledì 21 gennaio 2015
Mercoledì 21 gennaio 2015
Mercoledì 21 gennaio 2015
Giovedì 22 gennaio 2015
Giovedì 22 gennaio 2015
Giovedì 22 gennaio 2015
Venerdì 23 gennaio 2015
Venerdì 23 gennaio 2015
Venerdì 23 gennaio 2015
Venerdì 23 gennaio 2015
Venerdì 23 gennaio 2015
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 12:30, Aula seminari palazzina E, Dipartimento SBAI
Lo scopo della conferenza è di discutere alcuni problemi, legati ai concetti di continuità,
monotonia, proprietà del valor intermedio, ed esistenza di primitive. Tali problemi sono solo
apparantemente banali e ammettono a volte risposte sorprendenti, inaspettate, e in contraddizione
all'intuito geometrico. Come "effetto collaterale" della discussione presentiamo una serie di
esempi e controesempi che di solito non si possono trovare nei libri di analisi.
Ore 14:30, Aula di Consiglio
Seminario di Analisi Matematica
We consider the equation on R ipartial_t u -Delta u + chi |u|^2u = 0 where chi is a smooth function
decaying at infinity. The aim of this talk is to build an invariant measure for this equation
supported below L^2. We will in particular explain in which way it differs from the periodic setting
and the difficulties due to the infinite speed of propagation. This is a joint work with F.
Cacciafesta.
Ore 14:30, Aula 311, Università di Roma III
Seminario di Fisica Matematica
A review is given of the present status of superintegrable systems, i.e. finite dimensional
classical and quantum Hamiltonian systems with more integrals of motion than degrees of freedom. The
emphasis is on conceptual questions and on recent developments such as the discovery of infinite
families of superintegrable systems with integrals of motion of arbitrary order in the momenta.
Superintegrable systems involving particles with spin will be introduced
Ore 14:30, Aula Dal Passo, Università di Roma II
Seminario di Equazioni Differenziali
Ore 16:30, Aula D'Antoni, Università di Roma II
Seminario di Analisi Complessa
We apply a small part of Ecalles' "mould combinatorics" to the classical linearization problem of
non-resonant germs, which contains the well-known difficulties due to the so-called small divisor
phenomenon, and show that it yields compact formulas, from which one easily recovers the classical
analytical results of convergence of the solution under suitable arithmetical conditions on the
multiplier. We rediscover this way Yoccoz's lower bound for the radius of convergence of the
linearization and can even reach a sharp global regularity result with respect to the multiplier
(C1-holomorphy). Joint work with Frédéric Menous (Orsay U.) and David Sauzin (CNRS--Paris and SNS
Pisa),
Ore 14:30, Aula di Consiglio
Seminario di Algebra e Geometria
Multisymplectic structures are higher generalizations of symplectic structures, where forms of
higher degree are considered. We introduce a notion of moment map for such structures, based on
Stasheffu2019s notion of L-infinity algebra, and by relating it to equivariant cohomology we are
able to produce examples. Even though moment maps are quite involved, they admit a simple
cohomological description. Finally, we discuss some geometric implications of our moment maps (the
existence of conserved quantities).
Ore 16:00, Aula Dal Passo, Università di Roma II
Seminario di Analisi Complessa
Classifying regular systems of first order linear ordinary equations is a classical subject going
back to Poincare and Dulac. There is a gauge group whose action can be described and an integrable
normal form produced. A similar problem for higher order differential equations was never addressed,
perhaps because the corresponding equivalence relationship is not induced by any group action. Still
one can develop a reasonable classification theory, largely parallel to the classical theory. This
is a joint work with Shira Tanny from the Weizmann Institiute.
Ore 16:00, Aula Picone
Discussione di tesi di dottorato
Ore 16:00, Aula F, Università di Roma III
I tè di matematica
C'è un vasto filone, tra ricerca e didattica in matematica e nelle sue applicazioni,
riguardante i limiti e le potenzialità del computer su temi come l'approssimazione nel
calcolo numerico, la visualizzazione in geometria ed analisi o la modellazione. Partendo dalla
visualizzazione di alcuni problemi, cercherò di evidenziare come la distinzione tra didattica
e ricerca non sempre è (o dovrebbe essere) così netta: nello sforzo di trasmettere
quanto scoperto c'è un impegno didattico nel comunicare un risultato che può innescare
ulteriori approfondimenti ed aprirci a nuove domande. Tra i problemi trattati: poligoni costruibili
e rappresentazione per radicali, il rilievo per nuvole di punti e la modellazione in architettura,
la coesistenza di attrattori e la rappresentazione ottimale di un grafo.
Ore 16:15, Aula di Consiglio
Seminario di Fisica Matematica
The Lieb-Thirring inequality bounds the kinetic energy of a fermionic (i.e. anti-symmetric)
many-particle wave function in terms of its local particle density, and is an elegant and useful
combination of the uncertainty and the exclusion principles of quantum mechanics. Such a bound was
in work together with J. P. Solovej extended to more general identical particles, whose quantum
statistics can be modeled using bosons (i.e. symmetric functions) with a local repulsive
interaction, such as anyons in two dimensions. Here I consider the generalization and application of
similar energy bounds to a large family of pairwise interacting Bose gases. This is recent joint
work with F. Portmann and J. P. Solovej. I will also mention some work in progress, with P. T. Nam
and F. Portmann, concerning fractional-order operators and one-body interpolation inequalities.
Ore 0:00, Aula Picone
15:00 Senya Shlosman (CPT Marseille and Inst. for the Information Transmission Problems, RAS,
Moscow)
The case of N^{1/3} fluctuations in the 2D Ising model and the Airy diffusion.
I will consider the behavior of the phase separation interface of the 2D Ising model in the vicinity
of the wall. Scaled by N^{1/3}, it converges to the diffusion process, with a drift expressed via
Airy function. This process appeared earlier in Ferrari-Spohn study of Brownian motion, constrained
to stay outside circular barrier.
Joint work with D. Ioffe and Y. Velenik.
16:00 coffe break
16:30 Giorgio Fusco (Università de L'Aquila)
Platonic polyhedra, periodic orbits and chaotic motions in the N-body problem
We consider the N-body problem with interaction potential \alpha = |x_i-x_j|^{-\alpha}$ for
$\alpha\ge 1$. We assume that the particles have all the same mass and that N is the order |R| of
the rotation group R of one of the five Platonic polyhedra. We study motions that, up to a
relabelling of the N particles, are invariant under R. By variational techniques we prove existence
of periodic and chaotic motions. This is joint work with G. Gronchi and P. Negrini.
Ore 14:00, Aula di Consiglio
Seminario P(n): Problemi differenziali non lineari
We provide a simple method for obtaining new Liouville theorems (guaranteeing nonexistence of
positive entire solutions) for scaling invariant superlinear parabolic problems with gradient
structure. To illustrate the method we consider scalar and vector valued nonlinear heat equations
and the linear heat equation complemented by nonlinear boundary conditions. As a typical application
of our nonexistence results we provide universal estimates for positive solutions of related
problems in bounded and unbounded domains.
Ore 14:30, Aula 211, Università di Roma III
Seminario di Geometria
This talk surveys results on the singularities of the Minimal Model Program in a non-technical
manner and discusses applications to the study of varieties with trivial canonical class. A
classical Decomposition Theorem splits any compact Kähler manifolds with numerically trivial
canonical bundle into a product of a torus, a Calabi-Yau- and a holomorphic-symplectic manifold.
Building on extension theorems for differential forms on singular spaces, we prove an infinitesimal
version for singular varieties. In view of recent progress in minimal model theory, this can be seen
as a first step towards a structure theory for manifolds of Kodaira dimension zero. In the second
part of the talk we compare the étale fundamental group of a klt variety with that of its smooth
locus. As first major application, we show that any flat holomorphic bundle, defined on the smooth
part of a projective klt variety is algebraic and extends across the singularities. This allows to
generalise a famous theorem of Yau, which states that any Ricci-flat Kähler manifold with vanishing
second Chern class is an étale quotient of a torus. This is joint work with Daniel Greb and Thomas
Peternell
Ore 10:00, Aula 1B1, Dipartimento SBAI
Ore 11:30, Aula 311, Università di Roma III
Seminario di Logica e Geometria della Cognizione
La Ludica è un programma di ricerca iniziato da J.-Y. Girard nel 2001 allo scopo di fornire
un fondamento della logica basato sull'interazione. Attualmente, diversi studi sono condotti, che
guardano alla ludica come un modello computazionale del linguaggio naturale e, in particolare, del
dialogo. Lo scopo del seminario sarà introdurre gentilmente - anche attraverso qualche
esempio - a questo campo della ricerca.
Ore 12:00, Aula di Consiglio
Seminari MoMa
The unique electronic properties of graphene have attracted a huge amount of attention since its
discovery in 2004. The structural properties of such a two-dimensional lattice are less known but
not less exceptional. Graphene has a rippled anharmonic effects, has a peculiar phonon spectrum and
melts in a very unusual way. The structural properties of graphene are rather well described by bond
order classical potentials. We have shown in the past years that Monte Carlo simulations based on
such a potential (LCBOPII) can provide a detailed picture of the structure of graphene and of the
thermal long wavelength behaviour due to rippling and have compared our findings to continuum models
developed to describe two-dimensional membranes . The advantage of classical simulations is the
ability to deal with very large samples, allowing the study of localized (vacancies) and extended
defects (grain boundaries), melting, strain and frictional behavior. Examples will be shown in this
talk.
Ore 15:00, Aula Dal Passo, Università di Roma II
Seminario di Geometria Algebrica
The Clifford index of an algebraic curve behaves quite interestingly when the curve lies on a K3
surface. For example, it does not change if we let the curve move in its linear system. Moreover, if
the curve is non-general in moduli its Clifford index is always cut out by a linear system on the
surface. We will discuss a possible classification of these linear systems when the AMBIENT K3
surface carries non-symplectic automorphisms
Ore 15:30, Aula di Consiglio
Discussione di tesi di dottorato
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