University of Padua

Padua@thesis
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    Holomorphic functional calculus in non-Archimedean geometry

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    The purpose of this thesis is to provide a complete proof of the holomorphic functional calculus theorem for unital commutative Banach algebras over a non-Archimedean field KK, as introduced by V. G. Berkovich in the book "Spectral Theory and Analytic Geometry over Non-Archimedean Fields". Omitting some further properties that are proven, it says that there is a way to extend any bounded homomorphism ϕ ⁣:AD\phi\colon A\to D from a KK-affinoid algebra AA to a unital commutative Banach KK-algebra DD to a homomorphism \theta_\phi\colon \Gamma(\Sigma_\phi,O_{M(A)})\to \D, where Γ(Σϕ,OM(A))\Gamma(\Sigma_\phi,O_{M(A)}) is the KK-algebra of KK-affinoid functions on the spectrum of ϕ\phi.

    Cardinality and words in profinite groups

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    In this thesis, we study cardinalities and words in profinite groups. Let w = w(x1,...,xr) be a word, that is, an element of the free group on x1,...,xr. We are interested in the set of all the w-values in a group G, that is Gw = {w(g1,...,gr) : g1,...,gr ∈ G}, and the verbal subgroup w(G) generated by it. In particular we are interested in the sizes of these sets when w is a multilinear commutator word and G is a profinite group. A multilinear commutator word is a word obtained by nesting commutators and using each variable only once. For example the simple commutator [x, y] and more generally the higher commutators are multilinear commutator words. The goal of this thesis is to show that for a profinite group G and a multilinear commutator word w, if the cardinality of Gw is infinite then |Gw| = |w(G)| = 2a for some cardinal number a. The thesis is divided into three chapters. In the first one we will briefly introduce ordinal and cardinal numbers. In the second chapter we will show that the cardinal number of an infinite profinite group is 2a for some cardinal number a. In addition, we will prove that if a continuous map from a profinite group to a Hausdorff space has a "small image", then it is constant on a coset of a "big" closed subgroup. Finally in the third chapter we will collect some known results on multilinear commutator groups and we will prove our main results

    Teoremi di punto fisso ed equilibrio di Nash: applicazioni in ambito economico

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    La mia tesi espone dapprima risultati legati ai teoremi di punto fisso, successivamente applicazioni di questi risultati alla teoria dei giochi e infine delle applicazioni pratiche in ambito economico

    Progettazione di un braccio robotico per applicazioni spaziali integrato sul rover di Ateneo Morpheus

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    Nel presente elaborato viene illustrato il lavoro svolto per la progettazione e la realizzazione di un braccio robotico a quattro gradi di libertà da integrare sul rover di Ateneo. L'obiettivo principale di questo progetto di tesi consiste nello sviluppo di un manipolatore capace di posizionare l'end effector in un qualsiasi punto dello spazio di lavoro con una determinata posa, rispettando i requisiti funzionali scelti e i vincoli imposti

    Voter turnout and unemployment: the italian case

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