Dissertations / Theses: 'Plato's theory of Forms'

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Sinclaire, Jennifer. "The theory of forms and Plato's ethics." Master's thesis, University of Cape Town, 2012. http://hdl.handle.net/11427/11951.

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The aims of this dissertation are to uncover and analyse potential links between ethics and metaphysics - specifically, the theory of Forms - in the dialogues of Plato. Drawing on material from a wide range of Plato 's works, I investigate possible ways in which his theory of Forms might, at a very general level, converge with his moral theory.

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Chang, Kyung-Choon. "The role of Plato's Timaeus in the development of the Theory of Forms." Thesis, University of Cambridge, 1995. https://www.repository.cam.ac.uk/handle/1810/271962.

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Wiitala, Michael Oliver. "Truth and Falsehood in Plato's Sophist." UKnowledge, 2014. http://uknowledge.uky.edu/philosophy_etds/3.

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This dissertation is a study of the ontological foundations of true and false speech in Plato’s Sophist. Unlike most contemporary scholarship on the Sophist, my dissertation offers a wholistic account of the dialogue, demonstrating that the ontological theory of the “communing” of forms and the theory of true and false speech later in the dialogue entail one another. As I interpret it, the account of true and false speech in the Sophist is primarily concerned with true and false speech about the forms. As Plato sees it, we can only make true statements about spatio-temporal beings if it is possible to make true statements about the forms. Statements about the forms, however, make claims about how forms “commune” with other forms, that is, how forms are intelligibly related to and participate in one another. If forms stand in determinate relations of participation to other forms, however, then forms, as the relata of these relations, must compose structured wholes. Yet if they compose structured wholes, there must be a higher order normative principle that explains their structure. This creates a regress problem. In order to ground the structure of spatio-temporal beings, forms must be the highest explanatory principles. The theory of the “communing” of forms, however, makes it seem as if the forms require further explanation. This dissertation argues (1) that in the Sophist Plato solves the regress problem and (2) that, by doing so, he is able to ground true and false speech about the forms. I demonstrate that he solves the regress problem by differentiating a form’s nature from a form qua countable object. Then I show that this distinction between a form’s nature and a form qua countable object explains how true and false statements about the forms are possible.

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Baltzly, Dirk Christian. "Plato's argument from relatives : the role of the distinction between kath hauto and pros ti in the theory of forms /." The Ohio State University, 1992. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487777901657771.

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Snyder, Jacob T. "Reading Plato with Heidegger: A Study of the Allegory of the Cave." Kent State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=kent1334281162.

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Roche, Florentin. "Les niveaux psychologiques de Platon : une théorie de la connaissance d'après la cybernétique." Thesis, Lyon, 2017. http://www.theses.fr/2017LYSE3038.

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Cette recherche se propose de montrer l’existence de ce que nous appelons des « niveaux psychologiques » chez Platon, en empruntant à la théorie des types logiques, formulée par B. Russel et A.N. Whitehead, puis revisitée par l’anthropologue G. Bateson au sein du mouvement cybernétique. Par « niveaux psychologiques », nous entendons des états psychiques d’être en relation avec le réel sur le mode analogique. Nous défendons la thèse selon laquelle la théorie platonicienne des formes n’oblige pas à penser des degrés de réalité de la chose mais bien un processus de réalisation de l’objet en soi par le sujet de l’expérience. En tant que tels, les niveaux psychologiques correspondent donc à des niveaux d’apprentissages de la réalité. Ainsi, la méthode dialectique utilisée par Socrate accompagne le progrès de l’âme, pilotée par l’intellect, au moyen de la raison qui relie et distingue les phénomène sensibles. Cette double fonction caractérise l’exercice du langage et rend compte du mouvement de la pensée. La succession et la répétition des ajustements opérés à partir de l’expérience conduisent ainsi à une meilleure définition de la forme de l’objet en soi, i.e. une saisie plus nette de ce qui, de l’intelligible, passe dans le sensible. De ce fait, la théorie platonicienne de la connaissance apparaît comme une théorie du processus et non comme une théorie du contenu de savoir, qui mène du théâtre intérieur de nos représentations, limitées par le temps d’une vie et l’espace d’un corps, au spectacle de l’infini. En outre, parce qu’il existe un seul chemin pour penser ce qui est réellement, l’examen psychologique des causes de soi rejoint nécessairement la recherche philosophique sur les causes du monde, dans une cosmologie
This research intends to demonstrate the existence of what we call "psychological levels" in Plato's philosophy, taking from the theory of logical types, formulated by B. Russel and A.N. Whitehead, then restyled by the anthropologist G. Bateson, inside the cybernetic movement. By "psychological levels", we mean psychic states of being in relation with reality under an analogical scheme. We defend the argument that Plato’s theory of Forms does not imply degrees of reality in the thing but a process of realization of the object in itself through the subject experiencing it. As such, psychological levels refer to levels of learning what is reality. Thus, the Socratic dialectical method accompanies the soul’s progress, driven by the intellect, thanks to reason which relates and distinguishes the sensible phenomena. This double function characterizes what language is and gives reason for the movement of thought. Succession and repetition of the adjustments made from the experience of the thing lead to a better definition of the Form of the object in itself, i.e. a clearer acquisition of the intelligible part of the thing that is passing through its sensible expression. Hence, Plato’s theory of knowledge stands like a process theory more than a content theory, by conducting the search for truth from the inner theatre of our representations, limited by a lifetime and the space of a body, to the spectacle of the infinite. Furthermore, since there is only one path in order to think what exists in reality, the psychological research into the causes of thyself necessarily fits in the philosophical research into the causes of the world — a cosmology

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Bailey, Dominic Timothy John. "Cause, explanation and theory in Plato's Phaedo." Thesis, University of Cambridge, 2004. https://www.repository.cam.ac.uk/handle/1810/284040.

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This work is an investigation into a passage in Plato’s Phaedo in which Socrates tells his audience that, in the teeth of a certain difficulty, he can only establish the conclusion he wants - that the soul is immortal - if he comes up with a theory about coming to be and passing away generally. There then follows a discussion in which Socrates rejects the professed causes of those who had thought abut the matter before him, and then proceeds to outline his own method for getting at the truth. I begin in Section 1 with a detailed textual argument for the conclusion that the adjective αιτιον and the noun αιτια refer to logically different kinds of beings, a conclusion whose liability to misunderstanding leads me to a general discussion of Platonic teleology in Section 2. Section 3 argues at length against the thought that Socrates rejects the purported causes of others because of their susceptibility to logical controversies about opposites, concluding instead that he is using an epistemological indifference argument. The debate returns again to the details of the text in Section 4, where I arbitrate between two scholars in the debate about what exactly Socrates’ hypothesis is and how, as we are advised, we are to “hang on” to it in the course of inquiry. Section 5 dwells at length on an analogy between Plato and Frege, with a view to explaining what Socrates means when he recommends that would-be investigators conduct their research by looking in λογοι. Section 6 discusses the nature of the relation between a hypothesis and its results, arguing that Socrates’ inspiration for characterising the relation is drawn from Greek Harmonic Theory. Section 7 relates the epistemological themes considered so far to the question of whether any λογοι can turn true beliefs into knowledge, drawing the optimistic conclusion that they can, by way of an analysis of the image of the Sun in Republic VI. Section 8 considers at length what unhypothetical principles might be, and Section 9 concludes the work with an overview of Plato’s theory of explanation and justification, and how it relates to modern perspectives on those subjects.

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Sisson, Janet D. "The influence of mathematics on Plato's moral theory." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ54811.pdf.

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Morsella, Ricardo. "Concerning the Two Worlds Theory in Plato's metaphysical epistemology." Connect to online resource, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1442905.

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Gushue, Alison E. "A Comparison of Xenophon and Plato's Apologies." Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/cmc_theses/268.

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11

Hermannsson, Níels. "Plato's causal theory of the nature of man in the Timaeus, 69a6-92c9." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/23640.

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Timaeus 69a6-92c9 is a causal theory of the nature of man. Demigods, created heavenly bodies, take over soul and four elements, structured by a divine, good craftsman, who uses mathematical processes on things of two unlike origins. Imitating their creator, the demigods build man and leave him to run his life. What each individual man ‘takes over’ varies as does his individual and society’s handling of it, resulting in human lives ranging from the god-like to the murkiest low-life. This, through cycles of reincarnation, diversifies fauna bringing life, and extending the influence of reason into every elemental region; in a word it brings the heavens down to earth. Presented as anatomy, physiology, nosology and care of man, this is ancient Greek medical theory in the widest sense, including the use of hypothesis and claims about the soul. It mentions but stops short of addressing social and political levels. As cosmogony it is concerned with a micro-cosmos, but as cosmology with the running of this micro-cosmos within the macro-cosmos and as a part serving its overall being and purpose, as an organ serves and is served by the whole body of which it is an inner part. As a medical theory it brims with debated issues. Has Plato successfully answered the objections against using hypotheses, raised in On Ancient Medicine (Ch. III)? Is Aristotle’s objection to the theory of breathing a challenge to Plato’s analogy of macro- and micro cosmology? Why did Plato, unlike Galen later, chose to include soul in medicine, and to emphasise the elements, rather than the humours? Does movement as a cause of change and the different kinds of movements available for man’s self-care (Ch. V), mirror the intellectual and motivational division of human soul? Is the shaking receptacle a paradigm for vital human self-reflection? Chapter I discusses how introductions to English translations of the Timaeus reflect the old debate on keeping either to the heavens or to earth, to theology or to physics. Chapter II contains an introductory discussion on the Timaeus as a whole, with emphasis on its structure. In chapters III on anatomy, IV on physiology and in V on diseases and care of man, I focus on the structure of the causal account with regard to man as a mixed being. Using other texts purely for contrast and comparison I keep, to the extent possible, to the Timaeus, and mostly to 68e1-92c9. I argue that the transition between demiurgic and lesser gods’ causation at the junction of our main text and the previous lines, later carries over from the demigods to man’s self-care, individually and collectively, and that it mirrors the division of labour between Timaeus, Critias and Hermocrates, as natural philosophers, whereas Socrates, the fourth participant is a philosopher of a different kind along the line of division drawn at 29b. This thesis offers an outline of an argument for re-evaluating the Timaeus on the nature of man, particularly with regard to its formal logical side and its relation to rational persuasion.

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McQuillan, Daniel J. "Quadratic forms and Galois theory." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0013/NQ31148.pdf.

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Shao, You Yu. "Representation theory of quadratic forms /." The Ohio State University, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487858106116574.

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Fierro, María Angélica. "Plato's theory of desire in the Symposium and the Republic." Thesis, Durham University, 2003. http://etheses.dur.ac.uk/4110/.

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One of the main purposes of the Symposium is to describe the best and truest expression of Eros|epwg {the godSaiuwv and at the same time the affective disposition): Eros is an intermediary Saijucou between our mortal condition and what is divine and immortal. As such he malces us spontaneously feel attracted to beauty and through our procreating in it helps us to attain in this life 'a sort of immmortality by leaving behind our productions and, together with it, a certain ownership of the good, which is universally desired. Most people only attain a second grade of vicarious immortality, either through biological procreation or, in the best case, through cultural procreation. However, those who are able to follow a philosophical way of life might be able to contemplate Beauty itself and by procreating in it produce authentic virtue, in this way attaining ownership of the good as far as is possible for a human being in this life. But at the same time, it is hinted that a more permanent, god-lilce, existence might be available for the philosopher after death. In the light of the Republic some issues which remain unclear in the Symposium find an articulate explanation: a) The tripartite theory of the soul explains why, although everybody desires the good, different individuals focus their love and desire in different ways (even in a destructive way as is the case of the tyrant or of Alcibiades in the Symposium), b) The programme of earlier and higher education malces clear what the levels of the erotic ascent consist in. c) The nature of the Good helps us to understand the status of Beauty itself d) The myth of Er describes what a 'god-like', post mortem existence for the philosopher would be like, while also simultaneously, allowing for a different sort of 'immortality', along the lines suggested by the Symposium.

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Chaiyaporn, Chaiyan. "Plato's theory of man in relation to his political philosophy." Thesis, London School of Economics and Political Science (University of London), 1992. http://etheses.lse.ac.uk/1261/.

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It can be said that for Plato theory of man and political philosophy are tautologous. This study of Plato's theory of man points to the fact that a key concept in understanding Plato's political philosophy and man comes from the same source, that is , the concept of metaxy. The idea of metaxy is derived from the appreciation of the dialectic movement of arguments, speeches in the dialogues. The oscillation is argued to have been designed by the author of the dialogues in order to guide the reader to experience the existential moment with regard to the nature of the soul. The investigation of the Statesman, the Republic, the Phaedrus, the Symposium, and the Lysis, shows that the nature of man lies in the soul whose nature is metaxy. As regards the Platonic theory of the tripartite soul in the Republic, self-knowledge and the art of statesmanship are inseparable in the same way that the study of the soul and the city are intertwined. The philosopher must become king or statesman. As regards the idea of the pleasurable perception of rhythm and harmony in human nature in the Laws, dialectic and language of the philosopher-king are educational and political at the same time. The interplay of Dionysiac and Apollonian effects play an important role in understanding the metaxy of human nature and politics, or man and the city. However, the metaxy of politics entails the politics of metaxy, which renders a hermeneutic freedom to the reader, that is, he is free to choose or decide what kind of interpretation he is about to take or leave. Besides, the thesis claims a solution, which results from its study of human nature in the dialogues, to the enigmatic geometric riddles in the Statesman and the Republic.

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Tankha, Vijay. "The analogy between virtue and crafts in Plato's early dialogues /." Thesis, McGill University, 1990. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74591.

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This thesis investigates Plato's analogy between virtue and crafts, a comparison made extensively in the early dialogues. I first detail the model of technical knowledge that Plato uses as a paradigm of knowledge. An application of this model shows the inadequacies in some claims to know or to teach virtue. Applying the model to the Socratic dictum, 'Virtue is knowledge' enables us to understand what such knowledge is about. Such knowledge is identified as 'self-knowledge' and is the product of philosophy. Philosophy is thus revealed as the craft of virtue, directed at the good of individuals. One problematic aspect of the analogy between virtue and crafts is the possibility of misuse. Virtue conceived as self-knowledge enables Plato to explain both why such a craft cannot be misused and why it alone can be the basis for benefiting others.

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Franklin, Lee Aaron. "The role of language in Plato's theory of knowledge and learning /." The Ohio State University, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=osu1486398195325073.

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Jenney, Charles Davis. "A.F.C. Kollmann's theory of homophonic forms." Connect to resource, 1986. http://rave.ohiolink.edu/etdc/view.cgi?acc%5Fnum=osu1260458396.

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Sia, Charmaine Jia Min. "Structures on Forms of K-Theory." Thesis, Harvard University, 2015. http://nrs.harvard.edu/urn-3:HUL.InstRepos:17467390.

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In the early 1970s, Morava studied forms of topological K-theory and observed that they have interesting number theoretic connections. Until very recently, forms of K-theory have not been studied in greater depth and integrated into the modern theory of topological modular forms. In this dissertation, some expected structured ring spectra and locality results are established on forms of K-theory. Forms of algebraic structures are usually classified by Galois cohomology. Based on the structured ring spectra and locality results established, a criterion is given for distinguishing homotopy equivalence classes of forms of K-theory via a computation in the second homotopy group of the spectrum.
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Cohen, Sarah. "Height problems and modular forms." Thesis, University of Nottingham, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.353541.

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Beaugrand, Selina. "Bountiful mind : memory, cognition and knowledge acquisition in Plato's Meno." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/23451.

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The Meno has traditionally been viewed as "one of Plato's earliest and most noteworthy forays into epistemology." In this dialogue, and in the course of a discussion between Socrates and his young interlocutor, Meno, about the nature of virtue and whether it can be taught, “Meno raises an epistemological question unprecedented in the Socratic dialogues.” This question - or rather, dilemma - has come to be known in the philosophical literature as Meno’s Paradox of Inquiry, due its apparently containing an easy-to-detect equivocation of the word ‘know’. Immediately after the paradox, and in an apparent response to it, Socrates recounts a myth: a story told by priests and priestesses about the pre-natal existence and immortality of the soul. From this this myth, Socrates concocts the infamous theory of recollection – a theory according to which the soul has acquired knowledge of everything before it was born, while in a disincarnate state. According to the traditional reading of Meno’s paradox, this theory constitutes Plato’s response to it. The traditional reading has come under fire in recent years by advocates of the epistemological reading (ERM), who argue that the theory of recollection is not Plato’s intended response to the paradox. Instead, they suggest, Plato’s distinction between true belief and knowledge – which appears towards the end of the dialogue – is sufficient for solving the paradox; and as such, it ought to be read as Plato’s response to it. In this thesis, I argue against ERM’s claim that a mere epistemological distinction is all it takes to solve the paradox. To do so, I explore the metaphysics of change in Plato’s ontology. From this, I appeal to our everyday notion of ‘memory’ in order to show that Meno’s paradox, in fact, contains a hidden-premise, which when laid bare, reveals two distinct challenges contained within the argument: a superficial one, and a deeper one. I argue that although it appears at first blush as though the former could easily be dismissed as an equivocation, to which the epistemological distinction between belief and knowledge could provide an answer, the latter cannot. This is because the deeper challenge threatens the very preconditions of knowledge itself – that is to say, it renders cognition impossible – and, as such, it cancels out any effort to provide an epistemological response to the superficial challenge. Hence, unless the deeper-level challenge is satisfactorily disarmed, both challenges remain unanswered. I argue that although the major motivation for the theory of recollection in the Meno is indeed to provide an answer to scepticism about knowledge, nevertheless, it ought to be understood, first, as a theory of cognition – i.e. as a theory about the preconditions and atomic building blocks of knowledge – and not a theory of knowledge per se. This answer comes in the form of a radical theory of the mind and cognition – one that stands in stark opposition to our common-sense views about the mind: a view from which, Plato believed, the paradox arises. Drawing on recent debates between Nativists and Empiricists in the Cognitive Sciences, I argue that it was a great achievement of Plato’s to grasp that our common-sense view about the mind, and its concomitant process of learning, language acquisition and knowledge acquisition, might in fact be at the very root of scepticism about our ability to engage in meaningful philosophical practice, and our ability to acquire objective knowledge – especially, objective moral knowledge. The Meno’s paradox, then – so I contend - is not a puzzle whose solution rests upon merely pointing to an epistemological distinction between true belief and knowledge, as advocates of ERM have suggested. Rather, it is a puzzle about cognition. More precisely, it is a puzzle that targets the rudimentary cognitive stages of initial cognition and truth-recognition - one whose solution entails offering an account of the mind that would make these elementary cognitive processes possible. Accordingly, Plato’s theory of recollection in the Meno ought to be read as an attempt to map the structure of the mind, and as such, to provide an account of cognition. In doing so, he intended to put forward a view about the preconditions of knowledge – the sort of preconditions without which language acquisition and knowledge acquisition would simply not be possible. With this theory, Plato has the beginnings of an argument against the kind of relativism and scepticism prevalent at his time. As such, a correct interpretation of the so-called paradox of inquiry (and Plato’s proposed solution to it via the theory of recollection) should approach it as a puzzle about mind and cognition – and not solely as an epistemological one, as it has previously been treated.

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Belt, Dustin David. "Topics on the Spectral Theory of Automorphic Forms." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1423.pdf.

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McGillivray, Ivor Edward. "Some applications of Dirichlet forms in probability theory." Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.241102.

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Scotti, Simone. "Applications of the error theory using Dirichlet forms." Phd thesis, Université Paris-Est, 2008. http://tel.archives-ouvertes.fr/tel-00349241.

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This thesis is devoted to the study of the applications of the error theory using Dirichlet forms. Our work is split into three parts. The first one deals with the models described by stochastic differential equations. After a short technical chapter, an innovative model for order books is proposed. We assume that the bid-ask spread is not an imperfection, but an intrinsic property of exchange markets instead. The uncertainty is carried by the Brownian motion guiding the asset. We find that spread evolutions can be evaluated using closed formulae and we estimate the impact of the underlying uncertainty on the related contingent claims. Afterwards, we deal with the PBS model, a new model to price European options. The seminal idea is to distinguish the market volatility with respect to the parameter used by traders for hedging. We assume the former constant, while the latter volatility being an erroneous subjective estimation of the former. We prove that this model anticipates a bid-ask spread and a smiled implied volatility curve. Major properties of this model are the existence of closed formulae for prices, the impact of the underlying drift and an efficient calibration strategy. The second part deals with the models described by partial differential equations. Linear and non-linear PDEs are examined separately. In the first case, we show some interesting relations between the error and wavelets theories. When non-linear PDEs are concerned, we study the sensitivity of the solution using error theory. Except when exact solution exists, two possible approaches are detailed: first, we analyze the sensitivity obtained by taking "derivatives" of the discrete governing equations. Then, we study the PDEs solved by the sensitivity of the theoretical solutions. In both cases, we show that sharp and bias solve linear PDE depending on the solution of the former PDE itself and we suggest algorithms to evaluate numerically the sensitivities. Finally, the third part is devoted to stochastic partial differential equations. Our analysis is split into two chapters. First, we study the transmission of an uncertainty, present on starting conditions, on the solution of SPDE. Then, we analyze the impact of a perturbation of the functional terms of SPDE and the coefficient of the related Green function. In both cases, we show that the sharp and bias verify linear SPDE depending on the solution of the former SPDE itself

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Losonczy, Jozsef. "Combinatorial aspects of the theory of canonical forms." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/38411.

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Lei, Antonio. "Iwasawa theory for modular forms at supersingular primes." Thesis, University of Cambridge, 2010. https://www.repository.cam.ac.uk/handle/1810/226747.

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Let f=\sum a_nq n be a normalised eigen-newform of weight k\ge2 and p an odd prime which does not divide the level of f. We study a reformulation of Kato's main conjecture for f over the Zp-cyclotomic extension of Q. In particular, we generalise Kobayashi's main conjecture on p-supersingular elliptic curves over Q with a_p=0, which asserts that Pollack's p-adic L-functions generate the characteristic ideals of some \pm-Selmer groups which are cotorsion over the Iwasawa algebra \Lambda=Zp[[Zp]]. We begin by studying the p-adic Hodge theory for the p-adic representation associated to f in the case when a_p=0. It allows us to give analogous definitions of Kobayashi's \pm-Coleman maps and \pm-Selmer groups. The Coleman maps are used to show that the Pontryagin duals of these new Selmer groups are torsion over \Lambda as in the elliptic curve case. As a consequence, we formulate a main conjecture stating that Pollack's p-adic L-functions generate their characteristic ideals. Similar to Kobayashi's works, we prove one inclusion of the main conjecture using an Euler system constructed by Kato. We then prove the other inclusion of the main conjecture for CM modular forms, generalising works of Pollack and Rubin on CM elliptic curves. As a key step of the proof, we generalise the reciprocity law of Coates-Wiles and Rubin. Next, we study Wach modules associated to positive crystalline p-adic representations in general and generalise the construction of the Coleman maps. By applying this to modular forms with much more general a_p, we define two Coleman maps and decompose the classical p-adic L functions of f into linear combinations of two power series of bounded coefficients generalising works of Pollack (in the case a_p=0) and Sprung (when f corresponds to an elliptic curve over Q with a_p\ne0). Once again, this leads to a reformulation of Kato's main conjecture involving cotorsion Selmer groups and p-adic L-functions of bounded coefficients. One inclusion of this new main conjecture is proved in the same way as the a_p=0 case. Finally, we explain how the \pm-Coleman maps can be extended to Lubin-Tate extensions of height 1 in place of the Zp-cyclotomic extension. This generalises works of Iovita and Pollack for elliptic curves over Q.

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Hsu, Catherine. "Higher Congruences Between Modular Forms." Thesis, University of Oregon, 2018. http://hdl.handle.net/1794/23742.

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In his seminal work on modular curves and the Eisenstein ideal, Mazur studied the existence of congruences between certain Eisenstein series and newforms, proving that Eisenstein ideals associated to weight 2 cusp forms of prime level are locally principal. In this dissertation, we re-examine Eisenstein congruences, incorporating a notion of “depth of congruence,” in order to understand the local structure of Eisenstein ideals associated to weight 2 cusp forms of squarefree level N. Specifically, we use a commutative algebra result of Berger, Klosin, and Kramer to bound the depth of mod p Eisenstein congruences (from below) by the p-adic valuation of φ(N). We then show how this depth of congruence controls the local principality of the associated Eisenstein ideal.

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Zedda, Sergio. "Theory of proportion in Plato's Timaeus : the world-soul and the universe as structure." Thesis, University of Exeter, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.269829.

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Keet, Arnold Peter. "Topics in the algebraic theory of higher degree forms." Doctoral thesis, University of Cape Town, 1991. http://hdl.handle.net/11427/17338.

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Bibliography: pages 112-114.
Let d≥2 be an integer and let F be a field. A form of degree d over F is a polynomial of homogeneous degree d with coefficients in F. In degree d=2 there is an extensive theory of quadratic forms. We consider forms of degree d>2. The following are among the new results we have proved: 1. A nonsingular form over a field of characteristic zero has nonzero Hessian. This was proved by Harrison in degree d=3. We use some basic algebraic geometry and rational differential forms to give a proof valid in all degrees d≥2. 2. The formal differences of split forms constitute an ideal in the Grothendieck ring of higher degree forms. This generalises a well-known result for quadratic forms to higher degree. 3. In the monoid of equivalence classes of nondegenerate forms of degree d≥3, with the tensor product operation, the submonoid generated by the equivalence classes of the hyperbolic forms is free. This is a small step towards answering a question posed by Harrison. 4. Let the base field have characteristic zero. In every odd degree d≥3 there are no nontrivial families of additive invariants of the forms of degree d. In every even degree d there is a nontrivial family of additive invariants of the forms of degree d. The most familiar example is the family of discriminants of quadratic forms. Our proof involves the symbolic method for representing invariants of the forms of degree d. 5. We give a new proof, in characteristic zero, that a nonsingular form of degree d≥3 has a zero Lie algebra. Our proof involves a certain Schur functor and invokes the basis theorem of Akin, Buchsbaum and Weyman. 6. Let F be a field of characteristic zero and let K:F be a field extension. Let f be a form of degree d≥3 in more than three indeterminates with coefficients in F. Then if f is equivalent over K to a hyperbolic form, f must already be equivalent to a hyperbolic form over F. Compare this with the degree 2 case where, for example, the forms Σ(xk²+yk²) are hyperbolic over C but not over R.

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30

Gerken, Jan Erik. "Modular Graph Forms and Scattering Amplitudes in String Theory." Doctoral thesis, Humboldt-Universität zu Berlin, 2020. http://dx.doi.org/10.18452/21829.

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In dieser Dissertation untersuchen wir die Niedrigenergieentwicklung von Streuamplituden geschlossener Strings auf Einschleifenniveau (d.h. auf Genus eins) in einem zehndimensionalen Minkowski-Hintergrund mit Hilfe einer speziellen Klasse von Funktionen, den sogenannten modularen Graphenformen. Diese erlauben eine systematische Berechnung der Niedrigenergieentwicklung und erfüllen viele nicht-triviale algebraische- und Differentialgleichungen. Wir studieren diese Relationen detailliert und leiten Basiszerlegungen für eine große Zahl modularer Graphenformen her. Eines der Ergebnisse dieser Dissertation ist ein Mathematica-Paket, welches diese Vereinfachungen automatisiert. Wir benutzen diese Techniken, um die führenden Niedrigenergieordnungen der Streuamplitude von vier Gluonen im heterotischen String auf Einschleifenniveau zu berechnen. Für Stringamplituden auf Baumniveau bildet die Einwertigkeitsabbildung multipler Zetawerte offene Stringamplituden auf geschlossene Stringamplituden ab. Wir zeigen, dass ein bestimmter Vorschlag für die Definition einer geeigneten einschleifen-Verallgemeinerung, der sogenannten elliptische Einwertigkeitsabbildung, nicht alle Terme im heterotischen String reproduzieren kann. Ferner studieren wir eine Erzeugendenfunktion, die vermutlich die Torusintegrale aller perturbativen Theorien geschlossener Strings enthält. Wir bestimmen eine Differentialgleichung, die von dieser Erzeugendenfunktion erfüllt wird und lösen sie mit Hilfe von pfadgeordneten Exponentialen, was auf iterierte Integrale von holomorphen Eisensteinreihen führt. Da eine ähnliche Konstruktion im offenen String zur Verfügung steht, eröffnet dies außerdem eine neue Perspektive auf die elliptische Einwertigkeitsabbildung.
In this thesis, we investigate the low-energy expansion of scattering amplitudes of closed strings at one-loop level (i.e. at genus one) in a ten-dimensional Minkowski background using a special class of functions called modular graph forms. These allow for a systematic evaluation of the low-energy expansion and satisfy many non-trivial algebraic and differential relations. We study these relations in detail, leading to basis decompositions for a large number of modular graph forms which greatly reduce the complexity of the expansions of the integrals appearing in the amplitude. One of the results of this thesis is a Mathematica package which automatizes these simplifications. We use these techniques to compute the leading low-energy orders of the scattering amplitude of four gluons in the heterotic string at one-loop level. For tree-level string amplitudes, the single-valued map of multiple zeta values maps open-string amplitudes to closed-string amplitudes. The definition of a suitable one-loop generalization, a so-called elliptic single-valued map, is an active area of research and we show that a certain conjectural definition for this map, which was successfully applied to maximally supersymmetric amplitudes, cannot reproduce all terms in the heterotic string which has half-maximal supersymmetry. In order to arrive at a more systematic treatment of modular graph forms and at a different perspective on the elliptic single-valued map, we then study a generating function which conjecturally contains the torus integrals of all perturbative closed-string theories. We determine a differential equation satisfied by this generating function and solve it in terms of path-ordered exponentials, leading to iterated integrals of holomorphic Eisenstein series. Since a similar construction is available for the open string, this opens a new perspective on the elliptic single-valued map.

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31

Pallaver, Matteo. "Power and its forms : hard, soft, smart." Thesis, London School of Economics and Political Science (University of London), 2011. http://etheses.lse.ac.uk/220/.

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What is smart power? What kind of power is it? Is it really a new form of power? How many forms, features, and shapes does it take? How can we recognize and manage it? How do scholars describe it? This MPhil thesis aims to answer these and other questions regarding the dimension of power with a specific focus on smart power. This is a first attempt to study smart power in the broader context of power analysis and therefore I will follow two approaches. First of all, I will contextualize smart power, touching on the debate of power as an academic and political concept. Secondly, the idea is to investigate how power manifests itself in the realms of international and social relations. To this end, I will address three “ideal” forms of power, notably hard, soft and – finally - smart power. We already know that hard power is commonly associated in IR with realism: it is about power politics, force, and violence. Hard power is, to a certain extent, the oldest form of power; it is connected to the idea of an anarchic, untamed international system, where countries do not recognize any superior authority. Order is the result of competition for power and wars. The possession and acquisition of resources is the key to success. Soft power is something completely different. In order to understand soft power a methodological change is required. A state, an organization or a single person can exercise power with means other than violence and force. Persuasion, example, seduction, and myth: these are the resources of soft power. It is being able to convince or persuade others to follow your example, to want what you want, rather than coercing them. Soft power is about a world in which international institutions matter, in which war is not the only way to settle conflicts and in which the ones to succeed are the most powerful, in terms of natural, economic and financial resources and are not necessarily the best equipped. And finally, what is smart power? Where does it come from? We know that smart power is a new and to a certain extent popular concept, which was coined by Joseph Nye in the USA and is used to describe a new way of dealing with and managing power. Nye conceptualizes smart power as something lying somewhere between hard and soft power, a sort of “third way” in the complex jungle of power relations. But Nye also stresses that smart power is something “beyond” hard and soft, a sort of new approach that fits particularly well into the realm of international relations and foreign politics. This is why we will analyse Nye’s approach in depth, as well as the US debate about smart power and the concrete use of this concept by the US administration. Finally, we will investigate why smart power is becoming popular in the EU as well. Here again, policy-makers seem confident about using this new concept as a political programme that involves institutions and policy reforms. To sum up, my argument is that smart power is definitely a new form of power and this MPhil dissertation aims at introducing it into the academic debate, studying it from a theoretical, scientific point of view, investigating its origins, and the historical and political context in which it gained popularity and – finally – testing its possible declination in real scenarios of international politics.

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32

KANAYAMA, Yasuhisa (Yahei). "Recognition, Concept Formation and Knowledge: Preliminary Consideration for the Theory of Recollection in Plato's Phaedo." School of Letters, Nagoya University, 2013. http://hdl.handle.net/2237/17708.

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33

Myerson, Simon L. Rydin. "Systems of forms in many variables." Thesis, University of Oxford, 2016. http://ora.ox.ac.uk/objects/uuid:a9932e90-4784-466a-a694-d387c1228533.

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We consider systems of polynomial equations and inequalities to be solved in integers. By applying the circle method, when the number of variables is large and the system is geometrically well-behaved we give an asymptotic estimate for the number of solutions of bounded size. In the case of R homogeneous equations having the same degree d, a classic theorem of Birch provides such an estimate provided the number of variables is R(R+1)(d-1)2^d-1+R or greater and the system is nonsingular. In many cases this conclusion has been improved, but except in the case of diagonal equations the number of variables needed has always grown quadratically in R. We give a result requiring only d2^dR+R variables, obtaining linear growth in R. When d = 2 or 3 we require only that the system be nonsingular; when d<4 we require that the coefficients of the equations belong to a certain explicit Zariski open set. These conditions are satisfied for typical systems of equations, and can in principle be checked algorithmically for any particular system. We also give an asymptotic estimate for the number of solutions to R polynomial inequalities of degree d with real coefficients, in the same number of variables and satisfying the same geometric conditions as in our work on equations. Previously one needed the number of variables to grow super-exponentially in the degree d in order to show that a nontrivial solution exists.

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Candelori, Luca. "Towards a p-adic theory of harmonic weak Maass forms." Thesis, McGill University, 2010. http://digitool.Library.McGill.CA:8881/R/?func=dbin-jump-full&object_id=92409.

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Strömbergsson, Andreas. "Studies in the analytic and spectral theory of automorphic forms /." Uppsala : Matematiska institutionen, Univ. [distributör], 2001. http://www.ub.uu.se/acta/91-506-1456-8.pdf.

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36

Cofano, Marco. "Quantum field theory of (p,0)-forms on kaehler manifolds." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2013. http://amslaurea.unibo.it/5632/.

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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.

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37

Charles, S. R. "The emergent metaphysics in Plato's theory of disorder as found in The Timaeus and Laws X." Thesis, University of Edinburgh, 2003. http://hdl.handle.net/1842/4050.

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This thesis is an exploration of Plato’s understanding of the power of disorder as it is presented in his cosmology, The Timaeus and in his predominantly religious work, Laws X. In the former work this causal force is presented as the disordering power responsible for the physical chaos prior to the generation of the universe, as well as for any residual disorder found within the cosmos after it has been ordered and is the antithesis of ‘nous’ or reason. In the latter work, however, Laws X, the causal force for disorder is now understood as a disordering power capable of endangering the soul, active long after the cosmos has been generated and itself, a ‘Soul’. What ultimately emerges is a dynamic theory of disorder and a metaphysics supporting that theory, weaving through, connecting across and separating apart these two works. In Part I, consisting of five chapters, I provide the Greek, an original translation and commentary on seven key passages from The Timaeus where Plato presents his ideas on disorder, both as an effect within the cosmos and as a causal power or force for disorder prior to its generation. In this regard, I look closely at Plato’s use of the Greek word &V&YK~ in its role as a disordering power, but which has also been commonly understood and translated as ‘necessity’. I contrast this with Plato’s understanding of the role which the ‘Demiurge’ or the ordering power of the cosmos has played, with its faculty of ~06s or ‘reason’ and its access to ideal ‘Forms’ or ‘ideas’ when ordering or generating the universe. In Part 11, consisting of four chapters, Laws X is similarly presented, providing the Greek, a translation (for the most part, that of A. E. Taylor) and commentary on eight key passages. Here I investigate Plato’s understanding of disorder as it pertains specifically to the ‘soul’ and of the soul’s relation to the disordering power(s) and to ‘evil’. In the final chapter a theory of disorder is proposed, in which an epistemology is outlined, an ontology is given and from which, it is argued, a metaphysics of disorder emerges.

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38

Lynch, Tosca. "'Training the soul in excellence' : musical theory and practice in Plato's dialogues, between ethics and aesthetics." Thesis, University of St Andrews, 2013. http://hdl.handle.net/10023/4290.

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This thesis offers a technically informed examination of Plato's pervasive, though not innocent, use of musical theory, practice and musical concepts more generally within the ambitious ethical project outlined in many of his dialogues: fostering the ‘excellence' of the soul. Starting from Republic 3, Chapter 1 will focus specifically on music stricto sensu in order to assess Plato's interpretation of the basic ‘building blocks' of musical performances, creating a core repertoire of musical concepts that will prepare the way to analyse Plato's use of musical terms or categories in areas that, at first sight, do not appear to be immediately connected to this art, such as politics, ethics and psychology. Chapter 2 examines a selection of passages from Laws 2 concerning the concept of musical beauty and its role in ethical education, demonstrating how Plato's definition is far from being moralistic and, instead, pays close attention to the technical performative aspects of dramatic musical representations. Chapter 3 looks first at the harmonic characterisation of the two central virtues of the ideal city, sophrosyne and dikaiosyne, showing how their musical depictions are not purely metaphoric: on the contrary, Plato exploited their cultural implications to emphasise the characteristics and the functions of these virtues in the ideal constitution. The second half of Chapter 3 analyses the Platonic portrayal of musical παρανομία, studying both its educational and psychological repercussions in the dialogue and in relations to contemporary Athenian musical practices. Chapter 4 looks at how different types of music may be used to create an inner harmonic order of passions in the soul in different contexts: the musical-mimetic education outlined in the Republic, the musical enhancement of the psychological energies in the members of the Chorus of Dionysus in the Laws, and finally the role of the aulos in the Symposium.

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39

Vutha, Amit C. "Normal Forms and Unfoldings of Singular Strategy Functions." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1385461288.

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40

Nguyen, Manh Tu. "Higher Hida Theory on Unitary Group GU (2,1)." Thesis, Lyon, 2020. http://www.theses.fr/2020LYSEN009.

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Le travaux récent de Calegari et Geraghty ont enlevé les restrictions de la méthode originale de Taylor-Wiles, cela nous permet d’attaquer les conjectures de modularité plus générales. Leur méthode se fonde sur deux autres conjectures, l'une est reliée au problème d'attacher les représentations galoisiennes aux classes de torsion dans le groupe de cohomologie de la variété de Shimura sous entendue et l'autre à la dégrée de concentration de ces groupes de cohomologie localisés. La première conjecture a été adressée dans une grande généralité par Peter Scholze mais la seconde reste évasive. Récemment, pour la cohomologie cohérente, Vincent Pilloni a développé une version de la théorie de Hida pour les groupes de cohomologie supérieurs qui construit une interpolation p-adique du complexe de cohomologie en question. Comme une application importante, nous pouvons contourner la second conjecture au dessus et en effet dans un travail commun récent, Vincent Pilloni avec ses collaborateurs ont montré que toutes les variétés abéliennes sur un corps totalement réel est potentiellement modulaire. Dans cette thèse, nous adaptons l'argument de Vincent Pilloni pour construire un complexe qui interpole les classes de cohomologie supérieurs de la variété de Picard. Ces résultats servent comme le premier pas vers la modularité potentielle des variétés abéliennes de dimension 3 qui proviennent des Jacobiens de la courbe de Picard
In their breakthrough work, Calegari and Geraghty have shown how to bypass some serious restrictions of the original method by Taylor-Wiles, thus allowing us to attack more general modularity conjectures and related questions. Their method hinges on two conjectures, one is related to the problem of attaching Galois representations to torsion classes in the cohomology of Shimura varieties and the other to the requirement that these cohomology groups, localised at an appropriate ideal are non zero only in a certain range. The first conjecture is addressed in a great generality by Peter Scholze, but the second remains elusive. Recently, for coherent cohomology, inspired by the classical Hida theory, Vincent Pilloni has proposed a method consisting of p-adically interpolating the entire complex of coherent sheaves of automorphic forms on the Siegel threefold. This serves as a way to get around the second conjecture above and plays a crucial role in a recent work, where they show that abelian surfaces over a totally real field are potentially modular. In this thesis, we adapt the argument of Pilloni to construct a Hida complex interpolating classes in higher cohomology groups of the Picard modular surface. In a future work, we hope to use this to obtain some similar modularity results for abelian three-folds arising as Jacobians of some Picard curves

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41

Corbett, Andrew James. "Period integrals and L-functions in the theory of automorphic forms." Thesis, University of Bristol, 2017. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.723463.

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42

Shaughnessy, John F. "Finding Zeros of Rational Quadratic Forms." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/cmc_theses/849.

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In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. We begin by discussing Diophantine equations, the field of p-adic numbers, and the Hasse-Minkowski Theorem that allows us to use p-adic analysis determine whether a quadratic form has a rational root. We then discuss search bounds and state Cassels' Theorem for small-height zeros of rational quadratic forms. We end with a proof of Cassels' Theorem and suggestions for further reading.

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43

Thomas, O'Neill. "Differential Forms for T-Algebras in Kahler Categories." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/24217.

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A Kahler category axiomatizes the algebraic geometric theory of Kahler Differentials in an abstract categorical setting. To facilitate this, a Kahler category is equipped with an algebra modality, which endows each object in the image of a specified monad with an associative algebra structure; universal derivations are then required to exist naturally for each of these objects. Moreover, it can be demonstrated that for each T-algebra of said monad there is a natural associative algebra structure. In this paper I will show that under certain conditions on the Kahler category, the universal derivations for the algebras arising from T-algebras exist and arise via a coequalizer. Furthermore, this result is extended to provide an alternative construction for universal derivations for a more general class of algebras, including all algebras in a Kahler category. A prospective categorical formulation of the theory of noncommutative Kahler differentials is then given, and the above said results are shown to apply in this context. Finally, another class of algebras is constructed via a colimit, and the modules of differential forms for these algebras is computed.

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44

Babaian, Tamara. "Knowledge representation and open world planning using [Greek letter Psi]-forms /." Thesis, Connect to Dissertations & Theses @ Tufts University, 2000.

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Thesis (Ph.D )--Tufts University, 2000.
Adviser: James G. Schmolze. Submitted to the Dept. of Computer Science. Includes bibliographical references (leaves 148-156). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

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45

Zirkle, Laura. "Differentiating behaviors among Spillane's forms of distributed leadership." Thesis, Gannon University, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3607483.

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The purpose of this study was to identify what leadership behaviors are associated with each of Spillane's (2006) three conceptually distinct forms of distributed leadership, and to determine whether specific influence tactics (Yukl, Seifert & Chavez, 2008) are differentially associated with each form. A two-phased, mixed methods design was employed. The sampling frame for both phases included student affairs professionals in colleges and universities in New York, Ohio, and Pennsylvania, which were primarily four-year, undergraduate, co-educational, residential institutions. In Phase I, focus groups identified behaviors exhibited by student affairs professionals working together to accomplish a task. The identified behaviors were crafted into leadership behavior statements. These statements were triangulated with Spillane's forms of distribution: The co-investigator associated the statements with Spillane's conceptual definitions; while concurrently, a survey of these statements was sent to distributed leadership experts asking them to rate the expected likelihood of the behaviors being demonstrated in each of Spillane's forms of distributed leadership. Subsequently, in Phase II, student affairs professionals were surveyed regarding leadership behaviors and influence behaviors. Both cluster and factor analytic techniques were employed to associate influence behaviors with Spillane's forms of leadership distribution. Factor analysis of the leadership behaviors were interpreted in light of the co-investigator's cluster analysis of the same data. Spillane's distinct forms of distributed leadership were not affirmed by this study. When practicing distributed leadership – the idea that multiple participants co-create a leadership experience – a universal, differentiated view may be overly simplistic.

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46

Persson, Daniel. "Arithmetic and hyperbolic structures in string theory." Doctoral thesis, Universite Libre de Bruxelles, 2009. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210323.

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Résumé anglais:

This thesis consists of an introductory text followed by two separate parts which may be read independently of each other. In Part I we analyze certain hyperbolic structures arising when studying gravity in the vicinity of spacelike singularities (the BKL-limit). In this limit, spatial points decouple and the dynamics exhibits ultralocal behaviour which may be mapped to an auxiliary problem given in terms of a (possibly chaotic) hyperbolic billiard. In all supergravities arising as low-energy limits of string theory or M-theory, the billiard dynamics takes place within the fundamental Weyl chambers of certain hyperbolic Kac-Moody algebras, suggesting that these algebras generate hidden infinite-dimensional symmetries of gravity. We investigate the modification of the billiard dynamics when the original gravitational theory is formulated on a compact spatial manifold of arbitrary topology, revealing fascinating mathematical structures known as galleries. We further use the conjectured hyperbolic symmetry E10 to generate and classify certain cosmological (S-brane) solutions in eleven-dimensional supergravity. Finally, we show in detail that eleven-dimensional supergravity and massive type IIA supergravity are dynamically unified within the framework of a geodesic sigma model for a particle moving on the infinite-dimensional coset space E10/K(E10).

Part II of the thesis is devoted to a study of how (U-)dualities in string theory provide powerful constraints on perturbative and non-perturbative quantum corrections. These dualities are typically given by certain arithmetic groups G(Z) which are conjectured to be preserved in the effective action. The exact couplings are given by moduli-dependent functions which are manifestly invariant under G(Z), known as automorphic forms. We discuss in detail various methods of constructing automorphic forms, with particular emphasis on a special class of functions known as (non-holomorphic) Eisenstein series. We provide detailed examples for the physically relevant cases of SL(2,Z) and SL(3,Z), for which we construct their respective Eisenstein series and compute their (non-abelian) Fourier expansions. We also discuss the possibility that certain generalized Eisenstein series, which are covariant under the maximal compact subgroup K(G), could play a role in determining the exact effective action for toroidally compactified higher derivative corrections. Finally, we propose that in the case of rigid Calabi-Yau compactifications in type IIA string theory, the exact universal hypermultiplet moduli space exhibits a quantum duality group given by the emph{Picard modular group} SU(2,1;Z[i]). To verify this proposal we construct an SU(2,1;Z[i])-invariant Eisenstein series, and we present preliminary results for its Fourier expansion which reveals the expected contributions from D2-brane and NS5-brane instantons.

/

Résumé francais:

Cette thèse est composée d'une introduction suivie de deux parties qui peuvent être lues indépendemment. Dans la première partie, nous analysons des structures hyperboliques apparaissant dans l'étude de la gravité au voisinage d'une singularité de type espace (la limite BKL). Dans cette limite, les points spatiaux se découplent et la dynamique suit un comportement ultralocal qui peut être reformulé en termes d'un billiard hyperbolique (qui peut être chaotique). Dans toutes les supergravités qui sont des limites de basse énergie de théories de cordes ou de la théorie M, la dynamique du billiard prend place à l'intérieur des chambres de Weyl fondamentales de certaines algèbres de Kac-Moody hyperboliques, ce qui suggère que ces algèbres correspondent à des symétries cachées de dimension infinie de la gravité. Nous examinons comment la dynamique du billard est modifiée quand la théorie de gravité originale est formulée sur une variété spatiale compacte de topologie arbitraire, révélant ainsi de fascinantes structures mathématiques appelées galleries. De plus, dans le cadre de la supergravité à onze dimensions, nous utilisons la symétrie hyperbolique conjecturée E10 pour engendrer et classifier certaines solutions cosmologiques (S-branes). Finalement, nous montrons en détail que la supergravité à onze dimensions et la supergravité de type IIA massive sont dynamiquement unifiées dans le contexte d'un modèle sigma géodesique pour une particule se déplaçant sur l'espace quotient de dimension infinie E10/K(E10).

La deuxième partie de cette thèse est consacrée à étudier comment les dualités U en théorie des cordes fournissent des contraintes puissantes sur les corrections quantiques perturbatives et non perturbatives. Ces dualités sont typiquement données par des groupes arithmétiques G(Z) dont il est conjecturé qu'ils préservent l'action effective. Les couplages exacts sont donnés par des fonctions des moduli qui sont manifestement invariantes sous G(Z), et qu'on appelle des formes automorphiques. Nous discutons en détail différentes méthodes de construction de ces formes automorphiques, en insistant particulièrement sur une classe spéciale de fonctions appelées séries d'Eisenstein (non holomorphiques). Nous présentons comme exemples les cas de SL(2,Z) et SL(3,Z), qui sont physiquement pertinents. Nous construisons les séries d'Eisenstein correspondantes et leurs expansions de Fourier (non abéliennes). Nous discutons également la possibilité que certaines séries d'Eisenstein généralisées, qui sont covariantes sous le sous-groupe compact maximal, pourraient jouer un rôle dans la détermination des actions effectives exactes pour les théories incluant des corrections de dérivées supérieures compactifiées sur des tores.

Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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47

Raum, Martin [Verfasser]. "Dual weights in the theory of harmonic Siegel modular forms / Martin Raum." Bonn : Universitäts- und Landesbibliothek Bonn, 2012. http://d-nb.info/1044081236/34.

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48

Gerken, Jan Erik [Verfasser]. "Modular Graph Forms and Scattering Amplitudes in String Theory / Jan Erik Gerken." Berlin : Humboldt-Universität zu Berlin, 2020. http://d-nb.info/1217250107/34.

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49

Liu, Dunxue Carleton University Dissertation Mathematics. "Dihedral polynomial congruences and binary quadratic forms: a class field theory approach." Ottawa, 1992.

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Cunha, Ana Torre do Valle de Arriaga e. "Cumulative prospect theory : a parametric analysis of the functional forms and applications." Master's thesis, Instituto Superior de Economia e Gestão, 2012. http://hdl.handle.net/10400.5/10990.

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Abstract:

Mestrado em Finanças
Este trabalho apresenta um estudo empírico sobre cumulative prospect theory através do estudo da função de utilidade e a função de probabilidade distorcida. Os resultados obtidos estão de acordo com a literatura, que mostra que a função da utilidade é côncava no domínio dos ganhos, e quase linear no domínio das perdas. Não só mostra que a função da probabilidade distorcida tem a forma de um "S" inverso tanto no domínio dos ganhos como no domínio das perdas. Também aborda o estudo de variáveis demográficas relacionando-as com os coeficientes das funções mencionadas anteriormente, concluindo assim que os homens estão mais dispostos a correr riscos do que as mulheres. Por fim, através dos coeficientes calculados, foi possível aplicar os resultados ao mercado financeiro. Primeiro criando uma ponte entre o coeficiente de loss aversion e a escala de DOSPERT, o que irá facilitar a determinação do carteira mais adequado para cada individuo. Segundo, aplicando a cumulative prospect theory à modern portfolio theory para o mercado Português. Isto irá permitir que as instituições financeiras consigam determinar a carteira óptima do mercado, tendo em conta as probabilidades distorcidas.
This work presents an empirical study of the cumulative prospect theory using a Portuguese sample. We estimate the value function and the probability weighting function with positive and negative outcomes. The results confirm previous works that the value function is concave in the gain domain and almost linear in the loss domain. Our results also show an inverse S-shape for the probability weighting function in both loss and gain domain. We also look into the relation of the coefficient from the already mentioned functions with some demographic variables. It was possible to conclude that males are more willing to take risks than females. Finally, using the calculated coefficients we discuss the applicability of the results in the context of financial markets. First we establish a bridge between the loss aversion coefficient and the DOSPERT-scale, which will provide an easier way for financial institutions to present the correct efficient portfolio for each individual. Second we apply the cumulative prospect theory to the modern portfolio theory, for the Portuguese market. This will allow the financial institutions to create an efficient portfolio of the market, taking into account the probabilities distortions

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