Weighted Inequalities and Lipschitz Spaces

In this thesis I have characterized the trace measures for particular potential spaces of functions defined on R^n, but "mollified" so that the potentials are de facto defined on the upper half-space of R^n. The potential functions are kind Riesz-Bessel. The characterization of trace measures for these spaces is a test condition on elementary sets of the upper half-space. To prove the test condition as sufficient condition for trace measures, I had give an extension to the case of upper half-space of the Muckenhoupt-Wheeden and Wolff inequalities. Finally I characterized the Carleson-trace measures for Besov spaces of discrete martingales. This is a simplified discrete model for harmonic extensions of Lipschitz-Besov spaces.

Celestial Church of Christ in Italia. Percorsi, Spazi e Pratiche Rituali

Il lavoro che presento propone un’analisi di una chiesa africana indipendente in Italia, la Celestial Church Of Christ Worldwide (CCCW), cercando di mettere in luce il nesso tra religione, migrazione e il processo di ‘plunting churches’ (Kooning 2009) nel contesto italiano. Attraverso una ricerca sul campo, sono stati indagati i percorsi personali, familiari e comunitari dei membri di una ‘Celestial Parish’ presente nel comune di Brescia, ‘Ileri Oluwa Parish’, al fine di comprendere la natura dei processi identitari coinvolti nell’organizzazione della CCC in Italia. ‘Ileri Oluwa Parish’, in quanto luogo che denota una ‘chiesa individuale collegata ad una Diocesi’ (CCC Constitution (CCC Constitution, 107 (d) si rivela, nella materialità delle sue forme e dei ‘Devotional Services’ che in essa si svolgono, a ‘field of action’ (Lefebvre, 1991). La storia della chiesa, i fondamenti della sua dottrina e i significati comunicati attraverso le forme rituali e religiose che la stessa promuove, sono stati contestualizzati alla luce delle tensioni e delle strategie di potere che strutturano il campo. Le storie dei membri della parrocchia, percorsi di migrazione e mobilità in itinere, rappresentano la lente attraverso cui si è guardato alle relazioni vissute nel nome dello ‘Spirito’, e alla percezione stessa di ciò che gli stessi Celestians definiscono sacro, santo, puro e impuro. Lo sguardo fisso alla vita ordinaria di una Celestial parish in Italia, esteso nell’ultima parte dell’elaborato alla Celestial parish londinese, è stato fondamentale per capire l’intreccio di relazioni spirituali, reti familiari e mobilità degli individui sul territorio italiano ed europeo, processo che ribalta la condizione diasporica della CCC, trasformando una condizione di dispersione in un valore aggiunto, nella possibilità di nuove traiettorie territoriali e spazi di presenza religiosa e socioeconomica.

Fellow travelers: an ethnographic study of the dynamics of inter-organizational collaboration

The research is a 13-months ethnographic field work on the early operations of a Multi-party alliance active in the global field of indoor positioning. The study aims to understand and investigate empirically the challenges that at the individual and group level influence the organizing principle guiding the alliance operations and evolution. Its contribution rests on the dynamics affecting ecosystems of innovation and collaborative spaces of value co-creation in inter-organizational projects.

Numerical invariants for measurable cocycles

The theory of numerical invariants for representations can be generalized to measurable cocycles. This provides a natural notion of maximality for cocycles associated to complex hyperbolic lattices with values in groups of Hermitian type. Among maximal cocycles, the class of Zariski dense ones turns out to have a rigid behavior. An alternative implementation of numerical invariants can be given by using equivariant maps at the level of boundaries and by exploiting the Burger-Monod approach to bounded cohomology. Due to their crucial role in this theory, we prove existence results in two different contexts. Precisely, we construct boundary maps for non-elementary cocycles into the isometry group of CAT(0)-spaces of finite telescopic dimension and for Zariski dense cocycles into simple Lie groups. Then we approach numerical invariants. Our first goal is to study cocycles from complex hyperbolic lattices into the Hermitian group SU(p,q). Following the theory recently developed by Moraschini and Savini, we define the Toledo invariant by using the pullback along cocycles, also by involving boundary maps. For cocycles Γ × X → SU(p,q) with 1of Zimmer, namely such cocycles come from representations PU(1,n) → SU(p,q) of the ambient group. As a consequence, there is no Zariski dense such cocycle when 1of PU(p,q). We show that maximal cocycles are reducible, namely that, modulo cohomology, their image is contained in a finite dimensional algebraic subgroup of PU(p,∞). Finally, we classify Zariski dense measurable cocycles Γ × X → G from finitely generated groups into Hermitian groups not of tube-type. Precisely, we show that the pullback of the Kahler class completely determines the cohomology class of such cocycles.

The Legacy of Frankenstein’s Creature: Monstrosity and Female Grotesque in Mary Shelley, Angela Carter and Jeanette Winterson

This English Literature thesis (European PhD EDGES – Women’s and Gender Studies – 34th cycle) is an investigation into the representation of the monstrous body according to the British writers Mary Shelley, Angela Carter and Jeanette Winterson. The main objective is to observe how the representation of the categories of monstrous, abject and grotesque in Western cultural imagination have been influenced across time and literary genres. In the novels of Shelley, Carter and Winterson, the monstrous subject is configured as an alternative to the anthropocentric ideal embodied by the normative subject, of which Victor Frankenstein is the paradigmatic exponent. Plus, there are places considered anti-topoi within which the monster acquires a situatedness and claims a voice, generating an opposed counter-narrative to the imaginary conveyed by the normative subject. Monstrosity outlined by Shelley in the novels Frankenstein and The Last Man constitutes the starting point of my research, aiming to observe how the discourse of the normative body vs. the anti-normative body intersects with the discourse of the spaces of the centre vs. the spaces of the margin. In Carter's novels The Passion of New Eve and Nights at the Circus, the monstrous female constitutes the embodiment of wills, desires and claims challenging the heteronormative system. The space of otherness in which Carter's monster-woman is confined becomes a possibility of reshaping identity for the Subject, deconstructing the logic of power that moulded her within society. Finally, Winterson creates two monstrous women in Sexing the Cherry and The Passion who move through urban spaces, going from the centre to the margins and testifying to the arbitrariness of the system and its weaknesses. Similarly, in Frankissstein, Winterson recovers Shelley's original novel and transforms it into a parodic and intertextual speculation on the fluidity of identity and the limits of transhumanism.

The Hitchin map for one-nodal base curves of compact type

Studying moduli spaces of semistable Higgs bundles (E, \phi) of rank n on a smooth curve C, a key role is played by the spectral curve X (Hitchin), because an important result by Beauville-Narasimhan-Ramanan allows us to study isomorphism classes of such Higgs bundles in terms of isomorphism classes of rank-1 torsion-free sheaves on X. This way, the generic fibre of the Hitchin map, which associates to any semistable Higgs bundle the coefficients of the characteristic polynomial of \phi, is isomorphic to the Jacobian of X. Focusing on rank-2 Higgs data, this construction was extended by Barik to the case in which the curve C is reducible, one-nodal, having two smooth components. Such curve is called of compact type because its Picard group is compact. In this work, we describe and clarify the main points of the construction by Barik and we give examples, especially concerning generic fibres of the Hitchin map. Referring to Hausel-Pauly, we consider the case of SL(2,C)-Higgs bundles on a smooth base curve, which are such that the generic fibre of the Hitchin map is a subvariety of the Jacobian of X, the Prym variety. We recall the description of special loci, called endoscopic loci, such that the associated Prym variety is not connected. Then, letting G be an affine reductive group having underlying Lie algebra so(4,C), we consider G-Higgs bundles on a smooth base curve. Starting from the construction by Bradlow-Schaposnik, we discuss the associated endoscopic loci. By adapting these studies to a one-nodal base curve of compact type, we describe the fibre of the SL(2,C)-Hitchin map and of the G-Hitchin map, together with endoscopic loci. In the Appendix, we give an interpretation of generic spectral curves in terms of families of double covers.

Decompositions of powers of quadratic forms

We analyze the Waring decompositions of the powers of any quadratic form over the field of complex numbers. Our main objective is to provide detailed information about their rank and border rank. These forms are of significant importance because of the classical decomposition expressing the space of polynomials of a fixed degree as a direct sum of the spaces of harmonic polynomials multiplied by a power of the quadratic form. Using the fact that the spaces of harmonic polynomials are irreducible representations of the special orthogonal group over the field of complex numbers, we show that the apolar ideal of the s-th power of a non-degenerate quadratic form in n variables is generated by the set of harmonic polynomials of degree s+1. We also generalize and improve upon some of the results about real decompositions, provided by B. Reznick in his notes from 1992, focusing on possibly minimal decompositions and providing new ones, both real and complex. We investigate the rank of the second power of a non-degenerate quadratic form in n variables, which is equal to (n^2+n+2)/2 in most cases. We also study the border rank of any power of an arbitrary ternary non-degenerate quadratic form, which we determine explicitly using techniques of apolarity and a specific subscheme contained in its apolar ideal. Based on results about smoothability, we prove that the smoothable rank of the s-th power of such form corresponds exactly to its border rank and to the rank of its middle catalecticant matrix, which is equal to (s+1)(s+2)/2.

A cohomological approach to Ruelle-Pollicott resonances and speed of mixing of Anosov diffeomorphisms

Given a transitive Anosov diffeomorphism on a closed manifold it is known that, for smooth enough observables, the system is mixing w.r.t. the measure of maximal entropy. Therefore, it makes sense to investigate the speed of decay of correlations and to look for the so-called Ruelle-Pollicott resonances, in order to determine a complete asymptotics for the decay of correlations. In this thesis we are able to find the first terms of that asymptotics and to prove an estimate for the speed of decaying of correlations. The proof is based on a surprising connection between the action of a transfer operator on suitable anisotropic Banach spaces of currents and the action induced by the Anosov map on the de Rham cohomology.