Quantum field theory of (p,0)-forms on kaehler manifolds

In questa tesi abbiamo studiato la quantizzazione di una teoria di gauge di forme differenziali su spazi complessi dotati di una metrica di Kaehler. La particolarità di queste teorie risiede nel fatto che esse presentano invarianze di gauge riducibili, in altre parole non indipendenti tra loro. L'invarianza sotto trasformazioni di gauge rappresenta uno dei pilastri della moderna comprensione del mondo fisico. La caratteristica principale di tali teorie è che non tutte le variabili sono effettivamente presenti nella dinamica e alcune risultano essere ausiliarie. Il motivo per cui si preferisce adottare questo punto di vista è spesso il fatto che tali teorie risultano essere manifestamente covarianti sotto importanti gruppi di simmetria come il gruppo di Lorentz. Uno dei metodi più usati nella quantizzazione delle teorie di campo con simmetrie di gauge, richiede l'introduzione di campi non fisici detti ghosts e di una simmetria globale e fermionica che sostituisce l'iniziale invarianza locale di gauge, la simmetria BRST. Nella presente tesi abbiamo scelto di utilizzare uno dei più moderni formalismi per il trattamento delle teorie di gauge: il formalismo BRST Lagrangiano di Batalin-Vilkovisky. Questo metodo prevede l'introduzione di ghosts per ogni grado di riducibilità delle trasformazioni di gauge e di opportuni “antifields" associati a ogni campo precedentemente introdotto. Questo formalismo ci ha permesso di arrivare direttamente a una completa formulazione in termini di path integral della teoria quantistica delle (p,0)-forme. In particolare esso permette di dedurre correttamente la struttura dei ghost della teoria e la simmetria BRST associata. Per ottenere questa struttura è richiesta necessariamente una procedura di gauge fixing per eliminare completamente l'invarianza sotto trasformazioni di gauge. Tale procedura prevede l'eliminazione degli antifields in favore dei campi originali e dei ghosts e permette di implementare, direttamente nel path integral condizioni di gauge fixing covarianti necessari per definire correttamente i propagatori della teoria. Nell'ultima parte abbiamo presentato un’espansione dell’azione efficace (euclidea) che permette di studiare le divergenze della teoria. In particolare abbiamo calcolato i primi coefficienti di tale espansione (coefficienti di Seeley-DeWitt) tramite la tecnica dell'heat kernel. Questo calcolo ha tenuto conto dell'eventuale accoppiamento a una metrica di background cosi come di un possibile ulteriore accoppiamento alla traccia della connessione associata alla metrica.

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.

The nematode parasite fauna in three odontocete species: Phocoena phocoena, Lagenorhynchus albirostris, Lagenorhynchus acutus from Northern Scotland and its relationships with diet composition

Food items and nematode parasites were identified from the stomachs of 42 individuals of Phocoena phocoena, 6 of Lagenorhynchus acutus and 8 of L. albirostris stranded off the coastal waters of Northern Scotland between 2004 and 2014. Post-mortem examinations have revealed heavy parasitic worm burdens. Four nematode species complex as Anisakis spp., Contracaeucum spp., Pseudoterronova spp., and Hysterothylacium spp. were recorded. Data on presence of the anisakid species in cetaceans, reported a significative relationship between the presence of Hysterothylacium and the month of host stranding; suggesting a decrease of larval H. aduncum abundance in the period between April and August due to a seasonal effect related to prey availability. Similarly, the parasite burden of the all anisakid genera was related to the year fraction of stranding, and a relationship statistically significant was found just for L. albirostris with an increase between April and October. This finding is explained by a seasonality in occurrence of white-beaked dolphins, with a peak during August, that might be related to movements of shared prey species and competition with other species (Tursiops truncatus). Geographical differences were observed in parasites number of all anisakid species, which was the highest in cetaceans from the East area and lowest in the North coast. The parasites number also increased significantly with the length of the animal and during the year, but with a significant seasonal pattern only for P. phocoena. Regarding diet composition, through a data set consisting of 34 harbour porpoises and 1 Atlantic white-sided dolphins, we found a positive association between parasite number and the cephalopods genus Alloteuthis. This higher level of parasite infection in squid from this area, is probably due to a quantitative distribution of infective forms in squid prey, an abundance of the final host and age or size maturity of squid.

Real forms of Lie algebras and Lie superalgebras

In questa tesi abbiamo studiato le forme reali di algebre e superalgebre di Lie. Il lavoro si suddivide in tre capitoli diversi, il primo è di introduzione alle algebre di Lie e serve per dare le prime basi di questa teoria e le notazioni. Nel secondo capitolo abbiamo introdotto le algebre compatte e le forme reali. Abbiamo visto come sono correlate tra di loro tramite strumenti potenti come l'involuzione di Cartan e relativa decomposizione ed i diagrammi di Vogan e abbiamo introdotto un algoritmo chiamato "push the button" utile per verificare se due diagrammi di Vogan sono equivalenti. Il terzo capitolo segue la struttura dei primi due, inizialmente abbiamo introdotto le superalgebre di Lie con relativi sistemi di radici e abbiamo proseguito studiando le relative forme reali, diagrammi di Vogan e abbiamo introdotto anche qua l'algoritmo "push the button".

Temperature effects on larval growth and survival in five species of Caribbean Echinoids

Under the global change scenario, the possible effects of ocean warming were investigated on the larvae of five species of Caribbean Echinoids: Echinometra lucunter, Echinometra viridis, Clypeaster rosaceus, Tripneustes ventricosus and Lytechinus williamsi. Their thermal tolerance was evaluated rearing them for six days under different temperature regimes (26, 28, 30, 32, 34, 36°C). The larval sensitivity to the treatments was evaluated on the base of survival and growth. The rearing at higher temperatures has revealed a great suffering state of the larvae by inducing both reduction of live larvae and abnormality in their development. The extent of impact of the treatments varied from species to species, evidencing different levels of thermal tolerance. Anyway, higher temperature treatments have shown a general lethal threshold at about 34°C for most of the species. As an exception, the lethal threshold of Echinometra species was 36°C, few larvae of which being still capable of survive at the temperature of 34°C. The studies have also analyzed the effect of water warming on the larvae growth in terms of size and symmetry. The results put in evidence the presence of a critical upper temperature (about 32°C) at which the larvae of all species reveal a great suffering state that translates in the reduction of size (i.e., of body, stomach and postero-dorsal arm) and abnormalities (i.e., strong difference in the lengths of the two postero-dorsal arms). As sea surface temperatures are predicted to increase of 4-5°C by 2100, the high percentage of abnormal larvae and their scarce survival observed at 32- 34°C treatments indicate that the early stages of these species could be affected by future global warming.

Transgenerational effects of temperature on egg and larval development in Cyprinodon variegatus

Transgenerational plasticity (TGP), a type of maternal effect, occurs when the environment experienced by one or both the parents prior to fertilization directly translates, without changing DNA sequences, into changes in offspring reaction norms. Evidence of such effects has been found in several traits throughout many phyla, and, although of great potential importance - especially in a time of rapid climate change - TGP in thermal growth physiology had never been demonstrated for vertebrates until the first experiment on thermal TGP in sheepshead minnows, who, given sufficient time, adaptively program their offspring for maximal egg viability and growth at the temperature experienced before fertilization. This study on sheepshead minnows from South Carolina and Connecticut investigates how population, parent temperature, and offspring temperature affect egg production, size, viability, larval survival and growth rates, whether these effects provide evidence of TGP, and whether and how they vary with length of exposure time (5, 12, 19, 26, 33 and 43 days) of the parents to the new experimental temperatures of either 26°C or 32°C. Several results are consistent with those obtained in the previous TGP study, which outline a sequence of events consisting of an initial adjustment period to the new temperatures, in which egg production decreases and no signs of TGP are present, followed by a shift to TGP (towards 26-33 days of exposure) in which parents start to produce more eggs which are better adapted to the new thermal environment. Other results present new information, such as signs of TGP in the parent temperature effect on egg sizes already around 20 days of exposure. The innovative idea of populations being able to adapt to rapidly shifting environments through non-genetic mechanisms such as TGP opens new possibilities of survival of species and will have important implications on ecology, physiology, and contemporary evolution.