Notiziario Scientifico
Notiziario dei Seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 29 febbraio al 6 marzo 2016
Lunedì 29 febbraio 2016
Ore 14:30, aula di Consiglio
Seminario di Analisi Matematica
Andrea Davini (Sapienza Università di Roma)
Convergence of the solutions of the discounted H-J equation
We consider a continuous coercive Hamiltonian on the cotangent bundle of
the compact connected manifold M which is convex in the momentum.
We prove that the viscosity solutions uλ of the
critical Hamilton-Jacobi equation with positive discount factor λ
converge uniformly, as λ goes to 0, to a specific solution
u0 of the limit equation. We characterize u0
in terms of Peierls barrier and projected Mather measures.
As a corollary, we infer that the ergodic approximation, as introduced
by Lions, Papanicolaou and Varadhan in 1987 in their seminal paper on
periodic homogenization of Hamilton-Jacobi equations, selects a specific
corrector in the limit. The talk is based on a joint work with A. Fathi,
R. Iturriaga and M. Zavidovique that will appear on Inventiones Mathematicae.
Martedì 1 marzo 2016
Ore 14:30, aula Dal Passo, Università di Roma Tor Vergata
Seminario di Equazioni Differenziali
Annalisa Cesaroni (Università di Padova)
Homogenization of a mean field game system in the small noise limit
Mean field game systems describe the behaviour of a large population of
identical agents who control their dynamics minimizing a cost which depends
on the distribution law of the individual states.
We consider the case in which the game takes place in a periodically
heterogeneous medium, and the dynamics of the agents is disturbed by a
(vanishing) white noise. We analyse the simultaneous effect of homogenization
(assuming then that the frequency of heterogeneities in the medium is going to
+∞) and of the small noise limit, for a 2nd order mean field games system
with local coupling and quadratic Hamiltonian. An interesting feature of the
problem is that generically the effective system loses the MFG structure.
Joint work with N. Dirr (Cardiff) and C. Marchi (Padova).
Martedì 1 marzo 2016
Ore 15:00, aula F
Seminario di Didattica e Storia della Matematica
Enrico Rogora (Sapienza Università di Roma)
Considerazioni critiche sui modelli statistici per l'analisi dei test
I modelli statistici utilizzati nell'analisi dei test sono stati sviluppati per
estrarre 'misure di abilità' dai risultati.
Nel seminario si discuteranno alcune limitazioni intrinseche di tali misure e
le possibili distorsioni nell'interpretazione dei dati che si possono originare
nel non considerarle.
Martedì 1 marzo 2016
Ore 16:00, aula Picone
Seminario per insegnanti (Piano Lauree Scientifiche)
Dario Benedetto (Sapienza Università di Roma)
Problemi di matematica 'contestualizzati'
Mercoledì 2 marzo 2016
Ore 14:30, aula di Consiglio
Seminario di Algebra e Geoetria
Dennis Gaitsgory (Harvard)
Classical and geometric Langlands for functions fields
Let X be a curve over a finite field Fq and G a reductive group.
On the automorphic side of Langlands one studies the moduli space
Y=BunG(X) of principal G-bundles on X.
The classical theory of automorphic functions studies the space of
functions on Y(Fq) - the set of Fq-points of Y. The geometric theory
studies the category of sheaves on Y defined of the algebraic closure
of Fq. Langlands correspondence aims to relate both of these problems
to the study of homomorphisms of the fundamental group of X to the
Langlands dual group of G.
In the talk we will explain what Langlands correspondence actually
says in each of these contexts and how the two problems, the classical
and the geometric, are related.
Giovedì 3 marzo 2016
Ore 14:15, aula di Consiglio
Seminario P(n)
Gianmaria Verzini (Politecnico di Milano)
Bifurcation and segregation in quadratic two-populations Mean
Field Games systems
We consider a two-populations stationary Mean Field Games system, which
describes Nash equilibria in differential games with identical players.
In these models, each population consists of a very large number of
indistinguishable rational agents, aiming at minimizing some long-time
average criterion. Via the Hopf-Cole transformation, such system reduces
to a semilinear elliptic one, for normalized densities. Firstly, we discuss
existence of nontrivial solutions; secondly, for selected families of
nontrivial solutions, we address the appearing of segregation in the
vanishing viscosity limit.
Venerdì 4 marzo 2016
Ore 10:30, aula riunioni (primo piano), IAC-CNR, via dei Taurini 19
Seminario di Matematica Applicata
Abdul Barakat (Ecole Polytechnique, France)
Mechanics and Atherosclerosis: From Cells to Smart Devices
The pathological complications of atherosclerosis, namely heart attacks and
strokes, are the leading cause of mortality in the world. We are interested
in understanding the development of atherosclerosis and in devising novel
treatments for the disease. To this end, we are studying the role of mechanics
in two central events in the development of atherosclerosis: dysfunction of the
endothelial cells that line blood vessels and the increased movement of leukocytes
from the bloodstream into the arterial wall. We are also investigating ways by
which today's treatments for atherosclerosis, most notably stent performance,
can be improved to minimize patient complications. Finally, we are exploring novel
therapeutic and diagnostic pathways including nanoparticle-based targeted drug
delivery and smart implantable devices. In this talk, I will provide an overview
of our work on: 1) endothelial cell mechanotransduction, 2) leukocyte-endothelial
interactions, 3) nanoparticle-based drug delivery, and 4) optimization of today's
stents and development of tomorrow's smart and communicating stents.
Venerdì 4 marzo 2016
Ore 14:00, aula B
Corso di Dottorato
Lorenzo Bertini (Sapienza Università di Roma)
Grandi Deviazioni, I
Venerdì 4 marzo 2016
Ore 15:00, aula INdAM
Control, Dynamics and PDE's
Pierre Cardaliaguet (Univ. Paris Dauphine)
The master equation and the mean field limit in mean field games
In this joint work with F. Delarue, J.M. Lasry and P.L. Lions,
we discuss the convergence of the Nash system for an N-Player differential
game as N tends to infinity and the mean field limit of the optimal
trajectories. The proof relies on the construction of a solution to the
master equation, a transport equation in the space of probability measures.
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seminari@mat.uniroma1.it
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