Notiziario Scientifico
Settimana dal 7 al 13 aprile 2014
Lunedì 7 aprile 2014
Lunedì 7 aprile 2014
Martedì 8 aprile 2014
Martedì 8 aprile 2014
Martedì 8 aprile 2014
Martedì 8 aprile 2014
Mercoledì 9 aprile 2014
Mercoledì 9 aprile 2014
Mercoledì 9 aprile 2014
Mercoledì 9 aprile 2014
Mercoledì 9 aprile 2014
Giovedì 10 aprile 2014
Giovedì 10 aprile 2014
Giovedì 10 aprile 2014
Venerdì 11 aprile 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 B
Ore 14:30, Aula di Consiglio
Seminario di Analisi Matematica
Following the method introduced by Evans y Gangbo to solve the classical Monge-Kantorovich mass
transport problem, in this lecture we present two mass transport problems obtained as limit when pto
infty of the solutions of some problem related with the p-Laplacian operator. The first one is an
optimal matching problem that consists in transporting two commodities to a prescribed location, the
target set in such a way that they match there and the total cost of the operation, measured in
terms of the Euclidean distance that the commodities are transported, is minimized. We show that
such a problem has a solution with matching measure concentrated on the boundary of the target set.
Furthermore we perform a method to approximate the solution of the problem taking limit as pto infty
in a system of PDès of p-Laplacian type. The second problem consists in moving optimally
(paying a transport cost given by the Euclidean distance) an amount of a commodity larger or equal
than a fixed one to fulfill a demand also larger or equal than a fixed one, with the obligation of
paying an extra cost of -g_1(x) for extra production of one unit at location x and an extra cost of
g_2(y) for creating one unit of demand at y. The extra amounts of mass (commodity/demand) are
unknowns of the problem. Our approach to this problem is by taking the limit as ptoinfty to a double
obstacle problem (with obstacles g_1, g_2) for the p-Laplacian. In fact, under a certain natural
constraint on the extra costs (that is equivalent to impose that the total optimal cost is bounded)
we prove that this limit gives the extra material and extra demand needed for optimality and a
Kantorovich potential for the mass transport problem involved.
Ore 14:30, Aula Dal Passo, Università di Roma II
Seminario di Equazioni Differenziali
Presenterò la teoria di De Giorgi-Nash-Moser estesa ad operatori integro-differenziali non
locali.
Ore 14:30, Aula 311, Università di Roma III
Seminario di Fisica Matematica
A class of non-equilibrium statistical mechanics models that can be exactly solved by duality will
be reviewed. The class includes both interacting diffusions (Brownian Energy Process) and
interacting particle systems (Inclusion Process). The exact solution is based on the link between
quantum spin chains and generators of Markov processes. The duality property arises a change of
representation of an underlying Lie-algebra. Some universal properties of non-equilibrium (e.g.
long-range correlations) will be shown as a consequence of the exact solution. The presentation will
be based on joint works with G. Carinci, C. Giberti, J. Kurchan, F. Redig.
Ore 15:30, Aula di Consiglio
Seminario di Modellistica differenziale numerica
In this talk, we will review some known results on the link between reachability analysis and
optimal control problems in the deterministic setting. We will show how this link can be used to get
a constructive way for the characterization of the epigraph of the value function of constrained
control problems, without assuming any controllability assumption. Some extensions of these results
to the stochastic setting will be also discussed.
Ore 16:00, Aula Dal Passo, Università di Roma II
Topological phases of matter can be used to build inherently fault-tolerant quantum computers. I
will give an introduction to this approach as pursued in Microsoft Station Q, where topological
quantum field theories and modular categories play an essential role.
Ore 11:00, Aula 1B1, Dipartimento SBAI
Seminario di Geometria
Sia H un grafo fissato. Il numero di Turan di H, ex(H,n), è il massimo
numero di spigoli che un grafo con n vertici può avere senza contenere
una copia di H. Il problema è aperto per i grafi bipartiti. Se H è un
grafo bipartito completo, allora esistono sia un lower bound, ottenuto con
metodi probabilistici, che un upper bound, congetturato essere sharp, per
ex(H,n). Grafi con parametri estremali risultano essere il più delle
volte derivanti da costruzioni geometriche (su campi finiti). In questo
seminario vorrei illustrare come, attraverso l'uso di un particolare tipo
di varietà algebriche su campi finiti, sia stato possibile migliorare il
lower bound per il numero di Turan di una famiglia di grafi bipartiti
completi.
Ore 14:00, Aula G
Corso di Dottorato
Ore 14:30, Aula 311, Università di Roma III
Seminario di Analisi e Sistemi Dinamici
The singular set of weak KAM solutions associated with mechanical systems on the n-torus has common
structural aspects with the analogous set for general Hamilton-Jacobi equations but also unexpected
specific features, some of which were detected in joint papers with P. Cannarsa, and Q. Zhang. In
this talk, we will discuss analogies and differences starting with the propagation of singularities
for weak KAM solutions in the supercritical case. Then, applying these results to the barrier
function we will see that, whenever zero is a limiting gradient at a singular point of such a
function, a homoclinic orbit with respect to the Aubry set is produced. Finally, we will analyze
different conditions ensuring the above limiting property of zero at a critical point.
Ore 14:30, Aula di Consiglio
Seminario di Algebra e Geometria
Nakajimàs quiver varieties are important geometric objects in representation theory that can
be used to give geometric constructions of quantum groups. Very recently, graded quiver varieties
also found application to monoidal categorification of cluster algebras. Nakajimàs original
construction uses geometric invariant theory. In my talk, I will give an alternative representation
theoretical definition of graded quiver varieties. I will show that the geometry of graded quiver
varieties is governed by the derived category of the quiver Q. This approach brings about many new
and surprising results: for instance, it turns out that a large class of quiver varieties has a very
simple geometry, indeed they are isomorphic to affine spaces. Also, I will explain that familiar
geometric constructions in the theory of quiver varieties, such as stratifications and degeneration
orders, admit a simple conceptual formulation in terms of the homological algebra of the derived
category of Q. If time permits, I will also explain interesting applications of our work to
desingularization of quiver Grassmannians.
Ore 16:00, Aula F, Università di Roma III
I tè di matematica
In matematica circolano diverse nozioni di bordo. Io ne introduco un'altra: quella di bordo di un
campo vettoriale - e, più in generale, multi-vettoriale. Con questo tè, cerco di
convincervi della sua sensatezza e della sua utilità; in particolare, essa consente di dare
una definizione della derivata esterna per dualità - definizione che io trovo più
soddisfacente.
Ore 11:00, Aula 1B1, Dipartimento SBAI
Seminario di Geometria
In this talk we will discuss some properties of abstract Schrodinger operators over parabolic
manifolds, and particularize them to the stability operator of a parabolic constant mean curvature
surface immersed in a 3-manifold that admits a Killing vector field. As an application, we will give
restrictions on the range of H such that some homogeneous 3-manifolds admit complete parabolic
stable surfaces with constant mean curvature H. This is a joint work with Joaquin Perez and
Magdalena Rodriguez.
Ore 14:00, Aula di Consiglio
Seminario P(n): Problemi differenziali non lineari
In this talk I will describe recent results regarding special decay properties of solutions to the
initial value problem associated to the k-generalized Korteweg-de Vries equation. These are related
with persistence properties of the solution flow in weighted Sobolev spaces and with sharp unique
continuation properties of solutions to this equation. If time allows I will talk on recent
extensions of some of the results above for higher order dispersive equations.
Ore 14:00, Aula B
Ore 12:00, Aula di Consiglio
Seminari MoMa
As required by information theory, channel codes with long code words are necessary building blocks
in a transmission system to achieve reliable communications with minimal power and maximal
throughputs over noisy physical channels. Nowadays capacity-achieving large random binary codes are
actually adopted in most telecommunication standards. The breakthrough that allowed their practical
use has been to substitute the optimal maximum likelihood decoding techniques at the receiver with
suboptimal iterative techniques based on u201cbeliefu201d propagation. Belief propagation is a
powerful inference technique working on graphs used in many different applications. Graph nodes are
associated to factors or constraints of the model while graph edges are associated to random
variables. Belief propagation algorithm proceeds by iteratively updating messages associated to the
random variables, according to the constraints imposed by nodes. In the framework of channel
decoding the graph nodes represent the deterministic, usually linear, code constraints. They are
either associated to a (binary) parity check sum, or to a repetition of the variable. Belief
propagation is initialized with a set of messages obtained from the noisy channel observations of
the transmitted bits and proceeds iteratively, updating the messages according to the code
constraints until convergence is reached. Most practically used codes are linear and binary codes,
so that messages propagated in the graph are binary messages usually represented with a single
scalar (the Log-Likelihood Ratio). In order to increase the throughput of communication systems, the
use of non binary codes is an attractive solution as each symbol can carry more information bits.
Non binary codes can be constructed over groups, rings, or fields and there is a vast literature on
the design of capacity achieving non binary codes. The extension of the application of belief
propagation to the non binary codes however poses several complexity problems as both message
representation and message updating at check node grows at least linearly with the cardinality of
the non binary alphabet and consequently exponentially with the increase of required throughput. In
this talk I will start by recalling the fundamental ideas and terminology beyond binary channel
coding constructions and corresponding iterative decoding with belief propagation and other
iterative techniques. I will then extend the concepts to non binary codes and summarize the main
algorithms and complexity problems related with them. I will then introduce a new algorithm, named
Analog Digital Belief Propagation (ADBP) which solves the complexity problems of belief propagation
for non binary codes. I will discuss the main properties of the algorithm, its possible extensions
and code design problems related to the adoption of this algorithm.
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