Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 54-56).

Light scalar fields such as axions and string moduli can play an important role in early-universe cosmology. However, many factors can significantly impact their late-time cosmological abundances. For example, in cases where the potentials for these fields are generated dynamically --- such as during cosmological mass-generating phase transitions --- the duration of the time interval required for these potentials to fully develop can have significant repercussions. Likewise, in scenarios with multiple scalars, mixing amongst the fields can also give rise to an effective timescale that modifies the resulting late-time abundances. Previous studies have focused on the effects of either the first or the second timescale in isolation. In this thesis, by contrast, we examine the new features that arise from the interplay between these two timescales when both mixing and time-dependent phase transitions are introduced together. First, we find that the effects of these timescales can conspire to alter not only the total late-time abundance of the system --- often by many orders of magnitude --- but also its distribution across the different fields. Second, we find that these effects can produce large parametric resonances which render the energy densities of the fields highly sensitive to the degree of mixing as well as the duration of the time interval over which the phase transition unfolds. Finally, we find that these effects can even give rise to a "re-overdamping" phenomenon which causes the total energy density of the system to behave in novel ways that differ from those exhibited by pure dark matter or vacuum energy. All of these features therefore give rise to new possibilities for early-universe phenomenology and cosmological evolution. They also highlight the importance of taking into account the time dependence associated with phase transitions in cosmological settings. In the second part of this thesis, we proceed to study the early-universe cosmology of a Kaluza-Klein (KK) tower of scalar fields in the presence of a mass-generating phase transition, focusing on the time-development of the total tower energy density (or relic abundance) as well as its distribution across the different KK modes. We find that both of these features are extremely sensitive to the details of the phase transition and can behave in a variety of ways significant for late-time cosmology. In particular, we find that the interplay between the temporal properties of the phase transition and the mixing it generates are responsible for both enhancements and suppressions in the late-time abundances, sometimes by many orders of magnitude. We map out the complete model parameter space and determine where traditional analytical approximations are valid and where they fail. In the latter cases we also provide new analytical approximations which successfully model our results. Finally, we apply this machinery to the example of an axion-like field in the bulk, mapping these phenomena over an enlarged axion parameter space that extends beyond those accessible to standard treatments. An important by-product of our analysis is the development of an alternate "UV-based" effective truncation of KK theories which has a number of interesting theoretical properties that distinguish it from the more traditional "IR-based" truncation typically used in the literature.

On construit de nouvelles connexions quantiques intégrables dans fibrés vectoriels au-dessus d'espaces de modules de surfaces de Riemann et de leurs généralisations sauvages, en utilisant deux approches différentes. Premièrement, on utilise la quantification par déformation pour construire de nouvelles connexions intégrables à partir d'Hamiltoniennes d'isomonodromie irrégulières, dans l'esprit de Reshetikhin de la dérivation de la connexion de Knizhnik-Zamolodchikov à partir des Hamiltoniennes de Schlesinger. Deuxièmement, on construit une version complexe de la connexion de Hitchin pour la quantification géométrique de l'espace de modules de Hitchin sur une surface de genre un, par rapport au groupe SL(2,C) et à des polarisations Kähleriennes, en complémentant l'approche par polarisations réelles de Witten. Finalement, on utilise la transformée de Bargmann pour dériver une formule pour la connexion de Hitchin-Witten dans le fibré vectoriel des sections holomorphes, et pour transformer l'action de Hitchin en une transformée sur l'espace de Segal--Bargmann, basée sur les états cohérents. / We construct new flat quantum connections on vector bundles over moduli spaces of Riemann surfaces and their wild generalisations, using two different approaches. Firstly, we use deformation quantisation to construct new flat connections from irregular isomonodromy Hamiltonians, in the spirit of Reshetikhin's derivation of the Knizhnik-Zamolodchikov connection from the Schlesinger Hamiltonians. Secondly, we construct a complex version of the Hitchin connection for the geometric quantisation of the Hitchin moduli space over a surface of genus one, with respect to the group SL(2,C) and to Kähler polarisations, complementing Witten's real polarisation approach. Finally, we use the Bargmann transform to derive a formula for the connection of Hitchin-Witten on the vector bundle of holomorphic sections, and to turn Hitchin's action into a transform on the Segal--Bargmann space, which relies on coherent states.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第22247号 / 理博第4561号 / 新制||理||1655(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 畑 浩之, 教授 田中 貴浩, 教授 川合 光 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

As shown by Zagier, singular moduli can be represented by the coefficients of a certain half integer weight modular form. Congruences for singular moduli modulo arbitrary primes have been proved by Ahlgren and Ono, Edixhoven, and Jenkins. Computation suggests that stronger congruences hold for small primes $p \in \{2, 3, 5, 7, 11\}$. Boylan proved stronger congruences hold in the case where $p=2$. We conjecture congruences for singular moduli modulo powers of $p \in \{3, 5, 7, 11\}$. In particular, we study the case where $p=3$ and reduce the conjecture to a congruence for a simpler modular form.

No description available.

No description available.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-06-08T15:28:34Z No. of bitstreams: 1 divaneaparecidademoraesdantas.pdf: 855862 bytes, checksum: e55bbef7c7060caa2ff49488eb611852 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-07-13T13:29:55Z (GMT) No. of bitstreams: 1 divaneaparecidademoraesdantas.pdf: 855862 bytes, checksum: e55bbef7c7060caa2ff49488eb611852 (MD5) / Made available in DSpace on 2016-07-13T13:29:55Z (GMT). No. of bitstreams: 1 divaneaparecidademoraesdantas.pdf: 855862 bytes, checksum: e55bbef7c7060caa2ff49488eb611852 (MD5) Previous issue date: 2012-03-08 / O principal objetivo do trabalho é estudar os Espaços de Moduli das Configurações de Desargues, e este estudo é baseado no artigo (AVRITZER; LANGE, 2002). Uma configuração de 10 pontos e 10 retas, chamada uma configuração 103,obtidas do clássico teorema de Desargues, é chamada uma configuração de Desargues. Muitos espaços de moduli, senão todos, são obtidos algebricamente através das variedades algébricas de quociente, por isso estudamos um pouco de Teoria Geométrica dos Invariantes, ações de grupos algébricos em variedades algébricas e mostramos que existe o quociente categórico de uma variedade algébrica X por um grupo finito G e quando ele é o espaço e moduli grosso. Além disso mostramos que quando a variedade algébrica é afim (resp. quase projetiva) o quociente categórico é uma variedade algébrica afim (resp. quase projetiva). Finalmente, provamos que o quociente categórico(MD,p) de ˇP3 pelo grupo finito S5 é o espaço de moduli grosso para as configurações de Desargues. / The main aim of this work is to study the moduli space of Desargues configurations and it was based in (AVRITZER; LANGE, 2002). A configurations of 10 points and 10 line of the classic Desargues Theorem is called a Desargues configuration. Many moduli spaces, if not all, are obtained algebraically through the quotient of algebraic varieties. So we have studied a little about Geometric Invariant Theory and actions of algebraic group on varieties. We have showed that there exist the categorical quotient of a algebraic variety X by a finite algebraic group G and that it is a coarse moduli space. Moreover, we have showed that if X is a affine (resp. quasi-projective) the categorical quotient is an affine (resp. quasi-projective) variety Finally, we proved that the categorical quotient (MD,p) of the ˇP3 by the algebraic group finite S5 is the moduli space coarse for the Desargues configurations.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2017-05-29T14:33:20Z No. of bitstreams: 1 williamfredericovasconcellossilva.pdf: 451866 bytes, checksum: bfeb4aa8aa637b66cf493889e77ebca1 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-05-29T19:47:08Z (GMT) No. of bitstreams: 1 williamfredericovasconcellossilva.pdf: 451866 bytes, checksum: bfeb4aa8aa637b66cf493889e77ebca1 (MD5) / Made available in DSpace on 2017-05-29T19:47:08Z (GMT). No. of bitstreams: 1 williamfredericovasconcellossilva.pdf: 451866 bytes, checksum: bfeb4aa8aa637b66cf493889e77ebca1 (MD5) Previous issue date: 2012-07-12 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O principal objetivo do trabalho é estudar a relação entre o espaço de Moduli de feixes de quádricas em Pn e o espaço de Moduli de formas binárias de grau (n + 1). Este estudo foi baseado no artigo (AVRITZER; LANGE, 2000). Em linhas gerais, um espaço de Moduli é uma variedade algébrica que parametriza uma coleção de objetos C, módulo uma relação de equivalência. No nosso caso, C é o conjunto de feixes de quádricas em Pn ou o conjunto de formas binárias de grau (n + 1), e a relação de equivalência é pertencer à mesma órbita pela ação de um grupo G. Para estabelecermos a relação entre esses espaços foi importante considerar o símbolo de Segre que é um invariante dos feixes de quádricas. Além disso, estudamos a forma normal, uma maneira de reescrever o feixe de quádricas, na qual conhecemos facilmente o símbolo de Segre. Estudamos ação de grupos, para podermos classificar um feixe de quádrica e uma forma binária como estável, semi-estável ou instável, e quociente categórico, já que os espaços de Moduli são obtidos através do quociente. / The main objective is to study the relationship between space Moduli of pencil of quadrics, and Moduli space of binary forms. This study was based on article (AVRITZER; LANGE, 2000). In general, a Moduli space is an algebraic variety that parametrizes a collection of objects C, modulo an equivalence relation. In our case, C is the set of pencil of quadrics or set of binary forms of degree (n + 1), and the equivalence relation is to belong to the same orbit by the action of a group G. To establish the relationship between these spaces is important to consider the Segre symbol of which is an invariant of pencils of quadrics. Furthermore, we studied the normal form, a way to rewrite the pencil of quadrics, which easily met the Segre symbol, action of groups, in order to classify a pencil of quadric and a binary form as stable or semistable unstable, and quotient categorical, since the spaces's moduli are obtained by quotient.

Pour toute courbe projective lisse C et théorie homologique orientée de Borel-Moore libre A, on construit un produit associatif de type Hall sur les A-groupes du champ de modules des faisceaux de Higgs de torsion sur C.On montre que l'algèbre AHa0C qu'on obtient admet une présentation de battage naturelle, qui est fidèle dans le cas où A est l'homologie de Borel-Moore usuelle.On introduit de plus les espaces de modules des triplets stables M(d,n), fortement inspirés par les variétés de carquois de Nakajima.Ces espaces de modules sont des variétés lisses symplectiques, et admettent une autre caractérisation comme les espaces de modules de faisceaux sans torsion stables encadrés sur P(T*C)$.De plus, on munit leurs A-groupes avec une action de AHa0C, qui généralise les opérateurs de modification ponctuelle de Nakajima sur l'homologie des schémas de Hilbert de T*C. / For a smooth projective curve C and a free oriented Borel-Moore homology theory A, we construct a Hall-like associative product on the A-theory of the moduli stack of Higgs torsion sheaves on C.We show that the resulting algebra AHa0C admits a natural shuffle presentation, and prove it is faithful when A is replaced with usual Borel-Moore homology groups.We also introduce moduli spaces of stable triples M(d,n), heavily inspired by Nakajima quiver varieties.These moduli spaces are shown to be smooth symplectic varieties, which admit another characterization as moduli of framed stable torsion-free sheaves on P(T*C).Moreover, we equip their A-theory with an AHa0C-action, which generalizes Nakajima's raising operators on the homology of Hilbert schemes of points on T*C.