Construction of Bridgeland stability conditions on a given Calabi-Yau threefold is an important problem and this thesis realizes the rst known examples of such stability conditions. More precisely, we construct a dense family of stability conditions on the derived category of coherent sheaves on a principally polarized abelian threefold X with Picard rank one. In particular, we show that the conjectural construction proposed by Bayer, Macr and Toda gives rise to Bridgeland stability conditions on X. First we reduce the requirement of the Bogomolov-Gieseker type inequalities to a smaller class of tilt stable objects which are essentially minimal objects of the conjectural stability condition hearts for a given smooth projective threefold. Then we use the Fourier-Mukai theory to prove the strong Bogomolov-Gieseker type inequalities for these minimal objects of X. This is done by showing any Fourier-Mukai transform of X gives an equivalence of abelian categories which are double tilts of coherent sheaves.

Let Y be a smooth complex projective Calabi{Yau threefold. Donaldson-Thomas invariants [Tho00] are integer invariants that virtually enumerate curves on Y. They are organised in a generating series DT(Y) that is interesting from a variety of perspectives. For example, well-known series in mathematics and physics appear in explicit computations. Furthermore, closer to the topic of this thesis, the generating series of birational Calabi-Yau threefolds determine one another [Cal16a]. The crepant resolution conjecture for Donaldson-Thomas invariants [BCY12] conjectures another such comparison result. It relates the Donaldson{Thomas generating series of a certain type of three-dimensional Calabi-Yau orbifold to that of a particular resolution of singularities of its coarse moduli space. The conjectured relation is an equality of generating series. In this thesis, I first provide a counterexample showing that this conjecture cannot hold as an equality of generating series. I then verify that both generating series are the Laurent expansion about different points of the same rational function. This suggests a reinterpretation of the crepant resolution conjecture as an equality of rational functions. Second, following a strategy of Bridgeland [Bri11] and Toda [Tod10a, Tod13, Tod16a], I prove a wall-crossing formula in a motivic Hall algebra relating the Hilbert scheme of curves on the orbifold to that on the resolution. I introduce the notion of pair object associated to a torsion pair, putting ideal sheaves and stable pairs on the same footing, and generalise the wall-crossing formula to this setting, essentially breaking the former in many pieces. Pairs, and their wall-crossing formula, are fundamentally objects of the bounded derived category of the Calabi-Yau orbifold. Finally, I present joint work with J. Calabrese and J. Rennemo [BCR] in which we use the wall-crossing formula and Joyce's integration map to prove the crepant resolution conjecture for Donaldson-Thomas invariants as an equality of rational functions. A crucial ingredient is a result of J. Rennemo that detects when two generating functions related by a wall-crossing are expansions of the same rational function.

This work concerns the construction of Calabi-Yau threefolds in codimension 4. Based on a study of Hilbert series, we give a list of families of Calabi-Yau threefolds which may exist in codimension 3 and codimension 4. Using birational methods, we construct Calabi-Yau threefolds that realize several of the listed families. The main result is that the cases we consider in codimension 4 lie in two different deformation components.

This thesis explores and examines the concept of the threefold Word of God in the theology of Karl Barth, particularly the third form of the Word of God, the gospel proclamation, and argues that this tertiary form of the Word of God is central to Barth’s own theology of the church. This thesis argues that Karl Barth revised the concept of the threefold Word of God in the later volumes of the Church Dogmatics, but did not seek to reject the concept nor reject Christ’s presence and God’s speech in the gospel declaration and in the life of the Christian community. This thesis argues that the threefold Word of God is a crucial element in Karl Barth’s vision of the church and an important theme for the whole of his theological project. Disregarded by the field of Barth studies and rejected by modern ecclesiologists, Barth’s description of the gospel declaration and its central role in the life together of the Christian community offers an important ecclesiological alternative to carry forward for both Reformed theology and modern ecclesiology. This dissertation makes three significant contributions. First, this thesis is the first of its kind to engage comprehensively with Karl Barth’s concept of the threefold Word of God and to make clear its later revision. Second, this dissertation offers a review of the contemporary scholarly literature related to Barth’s revision of the threefold Word of God, and addresses the theological and ecclesiological implications of this revision. Third, this dissertation makes a contribution to the fields of Barth studies and contemporary ecclesiology by arguing for the central place of the third form of the Word of God in Karl Barth’s conception of the Christian community.

In this paper, we study sections of a Calabi-Yau threefold fibered over a curve by K3 surfaces. We show that there exist infinitely many isolated sections on certain K3 fibered Calabi-Yau threefolds and the subgroup of the N´eron-Severi group generated by these sections is not finitely generated. This also gives examples of K3 surfaces over the function field F of a complex curve with Zariski dense F-rational points, whose geometric models are Calabi-Yau. Furthermore, we also generalize our results to the cases of families of higher dimensional Calabi-Yau varieties with Calabi-Yau ambient spaces.

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The central theme of this thesis is the application of mirror symmetry to the study of the arithmetic geometry of Calabi-Yau threefolds. It formulates a conjecture about the properties of the limit mixed Hodge structure at the large complex structure limit of an arbitrary mirror threefold, which is supported by a two-parameter example of a self-mirror Calabi-Yau threefold. It further studies the connections between this conjecture with Voevodsky's mixed motives. This thesis also studies the connections between the conifold transition and Beilinson's conjecture on the values of the L-functions at integral points. It carefully studies the arithmetic geometry of the conifold in the mirror family of the quintic Calabi-Yau threefold and its L-function, which is shown to provide a very interesting example to Beilinson's conjecture.

The work deals with education technology in the specific environment of Waldorf school with an emphasis on pedagogical traits of this school type. The theoretical part includes the explanation of the term {\clq}qeducational technology``, the brief characteristics of alternative schooling, its rise and development. The main accent is put on the Waldorf pedagogy, its recourses, contents, aims, specifics and history in the Czech Republic and Waldorf education worldwide. The practical part includes records from inspections of Waldorf classes and then a comparison of theory and praxis. Then this work compares a social climate of the Waldorf class and the class with a classical way of education by questionnaires to find out objective positives of Waldorf education.

This research seeks to establish a postfoundational practical theology and the corresponding narrative approach to the contextual experience narratives of Jeju women. Its approach helps the readers to understand the co-researchers’ interpreted experience and to open their future narratives. This research attempts to discover the privileged values, themes, and social-constructed meaning of the co-researchers’ narratives. The postfoundational epistemology, which is proposed by Van Huyssteen and the “Seven movements” proposed by J.C Müller, has been used as a guideline. The research begins with the co-researchers’ storied experiences as a basic source of context. The co-researchers' context of Jeju Island has a very unique tradition, culture, religion and history. In order to investigate how they interpret their experiences situated in their own contexts, the researcher not only considers Paul Ricoeur’s hermeneutic theory of three mimesis, composed of pre-figuration, configuration, and re-figuration, alongside social constructionism, but also employs Michael White’s narrative therapy theory of deconstruction and re-authoring conversation for delineating thickened and alternative stories. The examination of the research context of Jeju Island, its history of Sasamsageon, as well as its tradition and culture in chapter four are conducted for the purpose of understanding and discovering the necessary meaning of the co-researchers’ narratives and values. In order to listen to the Jeju women’s experience narratives in their contexts, I have chosen four people who have lived in Jeju Island for a long generation. According to the perspective of the narrative approach, an attempt is made to focus on the personal meaning-making that the co-researchers assign to specific events in their lives and on how the co-researchers tell the story of these meaning-making and interpret their experiences. These co-researchers’ stories are to say about their relationship with their families and communities. The stories also include some background of their lives, particularly concentrating on the recent struggles they experienced and their understanding of their own relationships with God. Based on the co-researchers’ narratives and the process of the research, in regard to the goal of this postfoundational narrative research, i.e., looking for the meaning of the co-researchers’ narratives and creating new meaning through discourse, in chapter six, I present not only the interpretation of what they say, but also the meaning and understanding of the co-researchers’ own stories that are developed by means of discoursing with the given context. This research is presented for how to cultivate the alternative interpretations, which allowed the co-researchers to explore preferred views of their futures through discourse and conversation. And then I explicate the three interventions and interactions used for empowering and opening to the better future. / Thesis (PhD)--University of Pretoria, 2014. / gm2014 / Practical Theology / unrestricted