Let K be a number field and let S be a finite set of places of K. A classical theorem of Shafarevich says that there are only finitely many K-isomorphism classes of elliptic curves over K with good reduction outside S. An effective version of this statement for K=Q was already proved by Coates. In the talk we discuss an extension to arbitrary number fields. We give explicit bounds and compare them with the one obtained by Coates. One of the important features of the result is that we view an elliptic curve as a purely geometric object which is natural and gives flexibility for further generalisations. This is joint work with R. von Känel and G. Wüstholz.
La geometria algebrica derivata permette di definire una versione derivata del loop space LX per uno schema X. Le funzioni su LX coincidono con il complesso di omologia di Hochschild su X, mentre quelle S^1-invarianti forniscono un modello per l'omologia ciclica di Connes di X. Useremo LX per dare una definizione (equivalente a quella standard) del carattere di Chern per oggetti classici su X (fibrati vettoriali, complessi perfetti etc). Una tale reinterpretazione permette generalizzazioni interessanti del carattere di Chern ad oggetti più esotici come le famiglie di dg-categorie, importanti in geometria e teoria di Hodge non commutative. Nel seminario si assumeranno solo conoscenze di geometria algebrica (non derivata). Tutti gli interessati sono invitati a partecipare.
Il quadro generale dell'intervento è una ricerca sulla possibilità di applicare anche ai codici sorgente dei programmi per calcolatore alcuni concetti, tecniche e teorie che sono state sviluppate in questi anni a proposito dei testi più tradizionali. L'intervento cerca quindi di rispondere a una domanda: se sia possibile un'estetica della programmazione. Non un'estetica degli artefatti digitali intesi come prodotti finali realizzati tramite computer e fruibili con i nostri sensi ("computer graphics", "computer music" [...]), ma proprio degli artefatti digitali primari, in sé stessi, allo stadio originario di codice sorgente. Più precisamente: è possibile produrre (scrivere) codice sorgente con intenti (metodi, contesti.) estetici? è possibile considerare (leggere) esteticamente del codice sorgente? A quali condizioni?
Concurrent Constraint Programming (CCP) is a well-established model for concurrency that builds upon operational and algebraic notions from process calculi and first-order logic. Bisimilarity is one of the central reasoning techniques in concurrency. The standard definition of bisimilarity, however, is not completely satisfactory for CCP since it yields an equivalence that is too fine grained. By building upon recent foundational investigations (stemmed from the theory of Reactive Systems), we introduce a labelled transition semantics and a novel notion of bisimilarity that is fully abstract with respect to the typical observational equivalence in CCP. This way we provide CCP with a new proof technique that is coherent with existing ones.
Joint work with Andres Aristizabal, Catuscia Palamidessi, Luis Pino, Frank Valencia.
Faces are important visual stimuli to social primates because they transmit information that can be used to identify an individual. The human visual system is required to categorize, identify and remember the thousands of faces that are encountered throughout life. According to a popular theory, this is achieved by encoding the distinctiveness of each face on a number of linear dimensions representing independent perceptual attributes. In this multidimensional space, known as "norm-based face space" the identity of a given face is represented by its deviation from the central norm (the average of all previously seen faces). A major advantage of this framework is that it can help clarify how the human brain perceives and recognizes faces. Although face space has received a great deal of recent attention in the adult human literature, it is virtually unexplored in young infants and nonhuman primates. Only a handful of studies have investigated face space in children with the youngest age group being children over 4 years. This is primarily due to the reliance on verbal responses as dependent variables in the experimental procedures. In this study, we will develop rigorous psychophysical methods to study the structure of face space in young, preverbal infants (6 and 9 months of age) and nonhuman primates (chimpanzees and rhesus monkeys).This research has broad health implications as it will provide a complete understanding of how face space develops in humans and provide, as such, a valuable baseline for understanding the impairments in face coding that manifest in Autism Spectrum Disorders (ASD).
Dr. Jess Taubert
Yerkes National Primate Research Center, Emory University, Atlanta
Prof. V Hugh Perry,
School of Biological Sciences, University of Southampton, Mail Point 840, LD80B
South Lab and Path Block, Southampton General Hospital
Tel: 023 8079 6968
Dirichlet spaces on H-convex sets in the Wiener space
High electron mobility in graphene is one of its most interesting properties for potential applications. Despite intensive efforts, both experimental and theoretical, we still have no complete understanding of main electron scattering mechanisms and main limiting factors restricting the mobility. It is clear that a long-range scattering is important since short-range scatterers with radius of potential smaller than the electron wavelength are irrelevant for massless Dirac fermions. Three most probable candidates are charge impurities, scattering by elastic deformations created by frozen ripples, and resonant scattering centers (the last case also deals with long-range effects due to divergence of the scattering length). I review a theory of these mechanisms, together with relevant experimental results and first-principle calculations. It seems that the resonant scattering is the best candidate but the issue requires further research. I discuss also peculiarities of electron transport in bilayer graphene and temperature dependence of resistivity for freely suspended graphene samples. In the latter case, two-phonon processes involving bending mode give probably the main contribution.
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