Cube Complexes and Virtual Fibering of 3-Manifolds.

Una 3-varietà si dice virtualmente fibrata se ammette un rivestimento finito che è un fibrato con base una circonferenza e fibra una superficie. In seguito al lavoro di geometrizzazione di Thurston e Perelman, la generica 3-varietà risulta essere iperbolica; un recente risultato di Agol afferma che una tale varietà è sempre virtualmente fibrata. L’ingrediente principale della prova consiste nell’introduzione, dovuta a Wise, dei complessi cubici nello studio delle 3-varietà iperboliche. Questa tesi si concentra sulle proprietà algebriche e geometriche di queste strutture combinatorie e sul ruolo che esse hanno giocato nella dimostrazione del Teorema di Fibrazione Virtuale.

La rima: dalla metrica alla pedagogia con un'indagine su Gianni Rodari

Questo lavoro si presenta come un’indagine pluridisciplinare fra metrica,linguistica,letteratura e didattica, in cui la rima n’è l’oggetto e il filo conduttore. Attraverso questa ricerca si tenta di mostrare la capacità della rima di costituire un ponte fra espressione e contenuto, di allargare così il bagaglio non solo linguistico del fruitore, ma anche quello conoscitivo. Partendo dall’ambito linguistico e metrico, si analizza in prima istanza, l’apporto pratico che la rima ha avuto nell’evoluzione delle lingue volgari indoeuropee, per poi diventare il mezzo più semplice e istintivo per strutturare il verso poetico. Si passa così da un contesto folklorico ad uno colto, percorrendo tutti i secoli della nostra storia letteraria. Nella seconda parte la materia metrica cede il posto a quella didattico – pedagogica, e il passaggio è facilitato dalla poesia novecentesca che rimette in discussione il ruolo della rima, e la vede come il mezzo perfetto d’associazione fra parole, non solo di suono, ma anche di senso. A questo risponde la teoria del “binomio fantastico” di cui si avvale Gianni Rodari per creare le sue filastrocche, ed educare divertendo i suoi alunni. La rima con la sua omofonia finale, col suo accostamento casuale, concentra l’attenzione del bambino su di se e lo fa entrare a contatto col mondo delle parole, con la potenza della lingua.

A study of two Languages for Active Objects with Futures

In computer systems, specifically in multithread, parallel and distributed systems, a deadlock is both a very subtle problem - because difficult to pre- vent during the system coding - and a very dangerous one: a deadlocked system is easily completely stuck, with consequences ranging from simple annoyances to life-threatening circumstances, being also in between the not negligible scenario of economical losses. Then, how to avoid this problem? A lot of possible solutions has been studied, proposed and implemented. In this thesis we focus on detection of deadlocks with a static program analysis technique, i.e. an analysis per- formed without actually executing the program. To begin, we briefly present the static Deadlock Analysis Model devel- oped for coreABS−− in chapter 1, then we proceed by detailing the Class- based coreABS−− language in chapter 2. Then, in Chapter 3 we lay the foundation for further discussions by ana- lyzing the differences between coreABS−− and ASP, an untyped Object-based calculi, so as to show how it can be possible to extend the Deadlock Analysis to Object-based languages in general. In this regard, we explicit some hypotheses in chapter 4 first by present- ing a possible, unproven type system for ASP, modeled after the Deadlock Analysis Model developed for coreABS−−. Then, we conclude our discussion by presenting a simpler hypothesis, which may allow to circumvent the difficulties that arises from the definition of the ”ad-hoc” type system discussed in the aforegoing chapter.

Differential forms on Carnot groups

The main goal of this thesis is to understand and link together some of the early works by Michel Rumin and Pierre Julg. The work is centered around the so-called Rumin complex, which is a construction in subRiemannian geometry. A Carnot manifold is a manifold endowed with a horizontal distribution. If further a metric is given, one gets a subRiemannian manifold. Such data arise in different contexts, such as: - formulation of the second principle of thermodynamics; - optimal control; - propagation of singularities for sums of squares of vector fields; - real hypersurfaces in complex manifolds; - ideal boundaries of rank one symmetric spaces; - asymptotic geometry of nilpotent groups; - modelization of human vision. Differential forms on a Carnot manifold have weights, which produces a filtered complex. In view of applications to nilpotent groups, Rumin has defined a substitute for the de Rham complex, adapted to this filtration. The presence of a filtered complex also suggests the use of the formal machinery of spectral sequences in the study of cohomology. The goal was indeed to understand the link between Rumin's operator and the differentials which appear in the various spectral sequences we have worked with: - the weight spectral sequence; - a special spectral sequence introduced by Julg and called by him Forman's spectral sequence; - Forman's spectral sequence (which turns out to be unrelated to the previous one). We will see that in general Rumin's operator depends on choices. However, in some special cases, it does not because it has an alternative interpretation as a differential in a natural spectral sequence. After defining Carnot groups and analysing their main properties, we will introduce the concept of weights of forms which will produce a splitting on the exterior differential operator d. We shall see how the Rumin complex arises from this splitting and proceed to carry out the complete computations in some key examples. From the third chapter onwards we will focus on Julg's paper, describing his new filtration and its relationship with the weight spectral sequence. We will study the connection between the spectral sequences and Rumin's complex in the n-dimensional Heisenberg group and the 7-dimensional quaternionic Heisenberg group and then generalize the result to Carnot groups using the weight filtration. Finally, we shall explain why Julg required the independence of choices in some special Rumin operators, introducing the Szego map and describing its main properties.

Regularity of solutions of the p-Laplace equation in the Heisenberg group

tbd

Micro-simulation models at neighbourhood scale: the interplay of agents, buildings, activities and transport.

Urban systems consist of several interlinked sub-systems - social, economic, institutional and environmental – each representing a complex system of its own and affecting all the others at various structural and functional levels. An urban system is represented by a number of “human” agents, such as individuals and households, and “non-human” agents, such as buildings, establishments, transports, vehicles and infrastructures. These two categories of agents interact among them and simultaneously produce impact on the system they interact with. Try to understand the type of interactions, their spatial and temporal localisation to allow a very detailed simulation trough models, turn out to be a great effort and is the topic this research deals with. An analysis of urban system complexity is here presented and a state of the art review about the field of urban models is provided. Finally, six international models - MATSim, MobiSim, ANTONIN, TRANSIMS, UrbanSim, ILUTE - are illustrated and then compared.