Notiziario Scientifico
Settimana dal 21 al 27 ottobre 2013
Lunedì 21 ottobre 2013
Lunedì 21 ottobre 2013
Lunedì 21 ottobre 2013
Martedì 22 ottobre 2013
Martedì 22 ottobre 2013
Martedì 22 ottobre 2013
Martedì 22 ottobre 2013
Martedì 22 ottobre 2013
Mercoledì 23 ottobre 2013
Mercoledì 23 ottobre 2013
Giovedì 24 ottobre 2013
Venerdì 25 ottobre 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
Presentazione delle tesi di dottorato
We study the motion of discrete interfaces driven by ferromagnetic interactions in a two-dimensional
periodic environment, by coupling the minimizing movements approach by Almgren, Taylor and Wang and
a discrete-to-continuous analysis. In the case of a homogeneous environment, recently treated by
Braides, Gelli and Novaga, the effective continuous motion is a flat motion related to the
crystalline perimeter obtained by Gamma-convergence from the ferromagnetic energies, with an
additional discontinuous dependence on the curvature, giving in particular a pinning threshold. In a
joint work with A. Braides, we show that, in general, the motion does not depend only on the
Gamma-limit, but also on geometrical features that are not detected in the static description. In
particular, we show how the pinning threshold is influenced by the microstructure and that the
effective motion is described by a new homogenized velocity. In the last part of the talk, I would
like to present also the results of an ongoing joint work with A. Braides: we use a discrete
approximation of the motion by crystalline curvature to define an evolution of sets from a single
point (nucleation) following a criterion of "maximization" of the perimeter, formally giving a
backward version of the motion by crystalline curvature.
Ore 15:10, Aula di Consiglio
Presentazione delle tesi di dottorato
Dislocations are line defects in crystals and they are considered the main mechanism of plastic
deformations in metals. We will consider straight dislocations, so that their positions are
completely identified by the intersections of the dislocation line with an orthogonal plane. In this
talk we will present a purely variational approach, based on Gamma-convergence, to the study of the
asymptotic behavior of the static energy induced by a finite system of dislocations as the atomic
scale goes to zero. For a special class of dislocations, the so-called screw dislocations, we derive
also an interaction between the defects, which drives their dynamics. The essential tool in all the
results we will present is given by the analogy between dislocations and vortices in
superconductors, studied within the Ginzburg-Landau framework. The results are obtained in
collaboration with R. Alicandro, A. Garroni and M. Ponsiglione.
Ore 16:00, Aula G
Seminario di Fisica Matematica
We consider the log-partition function of the anisotropic quantum Heisenberg model in a finite box
Lambda of the d-dimensional cubic lattice Z^d. Using Ginibre's random loop representation based on
the discrete version of the Wiener process we derive the asymptotic expansion of the log-partition
function when Lambda - > Z^d. The proof is based on the abstract cluster expansion method.
Ore 14:15, Aula D'Antoni, Università di Roma II
Seminario di Equazioni Differenziali
We are motivated by the study of the Microcanonical Variational Principle within the Onsager's
description of two-dimensional turbulence in the range of energies where the equivalence of
statistical ensembles fails. We obtain sufficient conditions for the existence and multiplicity of
solutions for the corresponding Mean Field Equation on convex and thin enough domains in the
supercritical (with respect to the Moser-Trudinger inequality) regime. This result is of independent
interest, since general existence results in the supercritical region were previously known only on
multiply connected domains. Then we study the structure of these solutions by the analysis of their
linearized problems and also obtain a new uniqueness result for solutions of the Mean Field Equation
on thin domains whose energy is uniformly bounded from above. Finally we evaluate the asymptotic
expansion of those solutions with respect to the thinning parameter and use it together with all the
results obtained so far to solve the Microcanonical Variational Principle in a small range of
supercritical energies where the entropy is eventually shown to be concave. This is a joint work
with Francesca De Marchis.
Ore 14:30, Aula B
Consider the Erdos-Renyi random graph on n vertices where each edge is present independently with
probability p = c/n, with c > 0 fixed. For large n, a typical realization locally behaves like the
Galton-Watson tree with Poisson offspring distribution with mean c. We discuss large deviations from
this typical behavior, within the framework of the local weak convergence introduced by
Benjamini-Schramm and Aldous-Steele. The associated rate function is expressed in terms of an
entropy functional on unimodular measures and takes finite values only at measures supported by
trees. Along the way, we present a new configuration model which allows one to sample uniform random
graphs with a given finite neighborhood distribution, provided the latter is supported by trees. We
also present a new class of unimodular random trees, which generalizes the Galton-Watson tree with
given degree distribution to the case of neighborhoods of arbitrary finite depth. This is joint work
with Charles Bordenave.
Ore 14:30, Aula 311, Università di Roma III
Seminario di Fisica Matematica
In recent years, quantum graphs have become useful models in quantum chaos as well as other areas of
physics. Most of the results, however, are concerned with one-particle quantum graphs only. In this
talk, we will introduce models of interacting many-particle systems on general compact quantum
graphs. The models will incorporate two types of interactions, singular interactions localised at
the vertices and contact interactions which are also present along the edges. Subsequently, we use
the developed models to discuss Bose-Einstein condensation in such systems. As a result, we show
that many-particle systems, interacting with singular external potentials only, exhibit condensation
if and only if the interaction is not fully repulsive. We then implement particle-particle
interactions and show that repulsive hardcore interactions suppress Bose-Einstein condensation. Most
importantly, this result holds independently of the singular interactions in the vertices.
Ore 15:00, Aula L
Dare un senso a un testo matematico pone una serie di problemi. Ad esempio: come rendere conto di
elementi programmatici, di contenuti "immanenti", che si rivelerano solo più tardi? Dalla
soluzione a questi problemi dipende la relazione tra matematica e storia della matematica, o l'idea
di cos'è e cosa dev'essere la cultura matematica. Affronteremo questi temi attraverso un
esempio storico (i dibattiti sulla lettura di Euclide negli anni '70) e attraverso gli sviluppi
filosofici del ventesimo secolo (l'ermeneutica, strettamente legata alla fenomenologia di Edmund
Husserl e Gian Carlo Rota).
Ore 18:00, Aula 311, Università di Roma III
Seminario di Logica e Geometria della Cognizione
Classical realizability is a technique for extracting computational content from classical proofs.
It was introduced by Krivine in the middle of the 1990's combining ideas from traditional Kleene
realizability and from logical translations from classical to intuitionistic logics. Its fundamental
contribution is to put the notion of interaction (between a proof and a counter-proof, or between a
program and its environment) in a central position explicitly. Subsequently, it provides
enlightening descriptions of the computational behaviour of classical tautologies as synchronization
mechanisms between threads of a program. In this talk, I will survey the fundamental ideas that lead
to the interactive study of proofs with the tools of classical realizability, in the original
framework of the lambda-calculus with control operators. I will show how these ideas relate to other
models for proof systems (games, ludicsÉ), how it can be extended to other models of computation and
what it can teach us about the ongoing question of the proof-program correspondence for concurrent
computation.
Ore 14:30, Aula di Consiglio
Seminario di Algebra e Geometria
Time ordered products are familiar objects: they appear in the Picard expansion of the solution of
linear differential equations, almost everywhere in quantum physics and more generally, in disguise,
in many computations in algebra, analysis and probability. There have have many advances recently in
their understanding from a pure algebraic (Lie and group-theoretical) point of view. The keywords
are: Rota-Baxter algebras, pre-Lie algebras, Lie idempotents. The talk will survey some of these
developments, their background, and insist on the underlying pre-Lie structures. (Based on joint
work with K. Ebrahimi-Fard).
Ore 16:00, Aula 2001, Università di Roma II
In a celebrated paper, Kawahigashi-Longo-Mueger proved that the representation category of a
conformal net with finite mu-index is modular. We will present a new proof of this result. On our
way, we will define the conformal blocks that a conformal net associates to higher genus Riemann
surfaces.
Ore 14:00, Aula di Consiglio
Seminario P(n): Problemi differenziali non lineari
Some applications of the Mountain Pass Theorem are given for the study of some quasilinear boundary
value problems.
Ore 11:00, Aula 311, Università di Roma III
Seminario di Logica e Geometria della Cognizione
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