Abstract
In questo seminario si studia il comportamento asintotico di equazioni di diffusione non lineari, in dimensione $n$, nell intervallo degli esponenti $p > (n - 2)/n$,
per dati iniziali di momento secondo momento limitato. In questo range di non linearità si determina la convergenza a profili di tipo Barenblatt in termini di entropia relativa di tipo Renyi, per soluzioni rinormalizzate ad ogni tempo rispetto al proprio mmento secondo.
L analisi mostra che la entropia di Renyi relativa presenta un decadimento migliore, per tempi intermedi, rispetto alla standard entropia di tipo Ralston-Newton usata di solito in questo contesto. Il risultato consegue dalla proprietà di concavità della Renyi entropy power, recentemente dimostrata in un lavoro congiunto con G. Savaré.

Abstract
In this talk I will discuss the contribution of points and curves on a K3 surface to the Chow ring. The Chow ring of a K3 surface remains mysterious and reflects the interplay between
the arithmetic and geometry of the surface.
Classical results as well as open conjectures will be explained.

Abstract
In this talk I will illustrate the main results from my Phd thesis study about the estimation of the effects of deposition and resuspension
phenomena on the airborne PM10 concentration levels in Urban areas.
I will show how analytical solutions of algebraic Turbulence models have been used to describe the wind recirculation inside a urban canyon and the vehicle wakes interaction. Results from numerical simulations

of the air flow generated by single vehicles with different geometries and

velocities and the derived profile laws for deposition and resuspension

factors will be reported. Finally, pollutant dispersion results, together

with estimations of PM10 concentration levels after the implementaion

of different reduction scenarios, will be shown.

Abstract
Propongo il punto di vista che le architetture software, che siano grandi e complesse o spicciole ( quickies , come dicono gli Americani)
devono essere basate su un certo modello di riproducibilita e verificabilita .

L argomento sviluppo di software include molti aspetti di un progetto: il version control , le infrastrutture di programmazione, il controllo
dell integrita di dati e di pipeline , e anche le parti sociologiche del progetto: il modo in cui i collaboratori communicano e progettano.

Offriro esempi di progetti (tratti dalla mia cariera di astrofisico e hacker) che hanno avuto successo e di grandi disastri, e suggeriro che
il classico modello di sviluppo nel mondo del software libero e ideale per lo sviluppo di software scientifico a tutti i livelli.

Abstract
The Cahn-Hilliard (CH) equation describes the phase separation taking
place in a binary alloy subject to a rapid cooling process. More
precisely, it governs the evolution of the (relative) concentration
difference between the two components of the material. This equation
was proposed by J.W. Cahn and J.E. Hilliard in the late Fifties. Since
then it has been analyzed by many authors. Also, it has been recently
used to model other phenomena arising, for instance, in modeling tumor
growth, image segmentation and population dynamics. However, the
original CH equation has a phenomenological nature and lacks of a
rigorous justification. At the beginning of the Nineties, G. Giacomin
and J. L. Lebowitz proved that the hydrodynamic limit of a phase
segregation (separation) process is a nonlocal variant of the CH
equation. More precisely, the so-called chemical potential depends on
the concentration through a nonlocal spatial operator characterized by
a suitable interaction kernel. Thus the physically well-justified CH
equation is actually an integro-differential equation, while the
original CH equation can be viewed as its local approximation. After
an overview on the CH equation, I intend to give a (hopefully) not too
technical presentation of some recent mathematical results on the
nonlocal case.

Abstract
Given a harmonic function defined on the unit ball of R^n, we discuss techniques to
obtain effective volume estimates on the tubular neighborhood of its critical sets.


We use a technique recently introduced by proff. Jeff Cheeger and Aaron Naber,
called quantitative stratification technique. It is based on approximate symmetries
of the function u at different scales. Studying how these approximate symmetries
interact with each other, we obtain the effective volume estimates.

These results
are described in a preprint available on arXiv.

We also discuss possible improvements
of the results using a refined quantitative differentiation argument and packing
estimates for semi-algebraic sets.

Abstract
It is well known that lower semicontinuity of functionals in
the supremal form F(u)=esssupx�¸ƒ¶ f(�Þu(x))is related to the
level-convexity of the supremand f . We adress the problem of
existence of solutions for the Dirichlet boundary problem in the lack
of this convexity condition relating it with some differential
inclusion problem. This is a joint work with E. Zappale.

Abstract
We wish to present some recent developments concerning the
solvability of some classes of quasilinear parabolic equations with
dynamic boundary conditions. We will describe issues from
well-posedness to the long time asymptotic behavior as time goes to
infinity (attractors, dimension estimates, etc). We will explain how
to derive new conditions which reflect an exact balance between the
internal and the boundary mechanisms involved, even when both the
nonlinear sources contribute in opposite directions. Blow up of
solutions will also be touched on.