Cette thèse se compose de trois chapitres. Dans Chapitre 1, en supposant la conjecture standard de Lefschetz, on démontre la conjecture de Hodge généralisée pour une sous-structure de Hodge de convieau 1 qui est le noyau du cup-produit avec une classe de cohomologie grosse. Dans Chapitre 2, nous établissons une décomposition de la petite diagonale de X × X × X pour une intersection complète de type Calabi-Yau X dans un espace projectif. Comme une conséquence, on déduit une propriété de dégénérescence pour le produit d'intersection dans son anneau de Chow des deux cycles algébriques de dimensions complémentaires et strictement positives. Dans Chapitre 3, on démontre qu'un automorphisme symplectique polarisé de la variété des droites d'une hypersurface cubique de dimension 4 agit trivialement sur son groupe de Chow des 0-cycles, comme prédit par la conjecture de Bloch généralisée.

A \emph{simple} $n$-\emph{Venn diagram} is a collection of $n$ simple intersecting closed curves in the plane where exactly two curves meet at any intersection point; the curves divide the plane into $2^n$ distinct open regions, each defined by its intersection of the interior or exterior of each of the curves. A Venn diagram is \emph{reducible} if there is a curve that, when removed, leaves a Venn diagram with one less curve and \emph{irreducible} if no such curve exists. A Venn diagram is \emph{extendible} if another curve can be added, producing a Venn diagram with one more curve. Currently it is not known whether every simple Venn diagram is extendible by the addition of another curve. We show that all simple Venn diagrams with $5$ curves or less are extendible to another simple Venn diagram. We also show that for certain Venn diagrams, a new extending curve is relatively easy to produce. We define a new type of diagram of simple closed curves where each curve divides the plane into an equal number of regions; we call such a diagram a \emph{face-balanced} diagram. We generate and exhibit all face-balanced diagrams up to and including those with $32$ regions; these include all the Venn diagrams. Venn diagrams exist where the curves are the perimeters of polyominoes drawn on the integer lattice. When each of the $2^n$ intersection regions is a single unit square, we call these \emph{minimum area polyomino Venn diagrams}, or \emph{polyVenns}. We show that polyVenns can be constructed and confined in bounding rectangles of size $2^r \times 2^c$ whenever $r, c \ge 2$ and $n=r+c$. We show this using two constructive proofs that extend existing diagrams. Finally, for even $n$, we construct polyVenns with $n$ polyominoes in $(2^{n/2} - 1) \times (2^{n/2} + 1)$ bounding rectangles in which the empty set is not represented as a unit square. / Graduate / 0405 / 0984 / bbultena@uvic.ca

This Dissertation covers three aspects of General Relativity: inequivalent Einstein metrics on Lie Group Manifolds, proving the Hoop Conjecture for Black Rings, and investigating ergoregions in magnetised black hole spacetimes. A number of analytical and numerical techniques are employed to that end. It is known that every compact simple Lie Group admits a bi-invariant homogeneous Einstein metric. We use two ansatze to probe the existence of additional inequivalent Einstein metrics on the Lie Group SU (n). We provide an explicit construction of 2k + 1 and 2k inequivalent Einstein metrics on SU (2k) and SU (2k + 1) respectively. We prove the Hoop Conjecture for neutral and charged, singly and doubly rotating black rings. This allows one to determine whether a rotating mass distribution has an event horizon, that it is in fact a black ring. We investigate ergoregions in magnetised black hole spacetimes. We show that, in general, rotating charged black holes (Kerr-Newman) immersed in an external magnetic field have ergoregions that extend to infinity near the central axis unless we restrict the charge to q = amB and keep B below a maximal value. Additionally, we show that as B is increased from zero the ergoregion adjacent to the event horizon shrinks, vanishing altogether at a critical value, before reappearing and growing until it is no longer bounded as B becomes greater than the maximal value.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第23676号 / 理博第4766号 / 新制||理||1683(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 森脇 淳, 教授 雪江 明彦, 教授 吉川 謙一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

This cultural research explores the relation between racial representation and emotions/affects as part of the struggle for racial minorities’ visibility. It is informed by conjunctural theory in cultural studies, with the use of textual narrative and affective analysis. It focuses on Hong Kong’s television culture as a site for context configuration, or conjuncture, for constructing the inter- and intra-ethnic relations between the dominant ethnic Chinese and ethnic minorities (EMs), via the production of emotions. Chapter One introduces a conjunctural understanding of the construction of EMs in Hong Kong through revisiting some of the most prominent theoretical works that explore the transformation of Hong Kong identity, in order to point out an underlying Hong Kong-Chineseness as a cultural center, and to argue that the demand of the present conjuncture is to respond to the necessity of generating an alternative “EM-context” suitable for reimagining Hong Kong identity. Chapter Two attempts to map out this “EM-context” by reviewing the major popular non-Chinese figures on TV, namely Louie Castro, Gregory Rivers (known as “Ho Kwok-wing”) and Gill Mohinderpaul Singh (known as “QBoBo”) in order to study how their particular cultural visibility can open up ways to rethink the problems surrounding visibility. The narrative affective approach to study racial relations is applied to the reading of No Good Either Way (TVB) in Chapter Three and Rooms To Let (RTHK) in Chapter Four. Together, these two core chapters explore the affective configuration of “anxieties” and “shame” in the two TV programmes. It is suggested that these affective landscapes help position EMs as either a “sweetened trouble-maker” (in the work place) or “assimilating neighbor” (in the domestic sphere), both of which fall short of being able to construct a new context/conjuncture for understanding the cultural presence of EMs. This research rejects the study of race/ethnicity through content analysis of stereotype, and opts for an approach that reads affects and narratives in the search not for representational visibility, but for what is termed “conjunctural visibility.” Ultimately, Chapter Five concludes with a discussion of the dynamics of “soft” and “hard” representations of the ethnic other: the former in the mode of “sugarcoated racism” which involves the figure of EM as the sweetened troublemaker appealing for audience’s sympathy, and the latter in the form of public pedagogy aimed at educating the audience (through shaming) to treat their EM neighbor as the assimilated other. This research study aims at making a small contribution to the understanding of the struggle for conjunctural visibility among EMs in Hong Kong.

abstract: The primary focus of this dissertation lies in extremal combinatorics, in particular intersection theorems in finite set theory. A seminal result in the area is the theorem of Erdos, Ko and Rado which finds the upper bound on the size of an intersecting family of subsets of an n-element set and characterizes the structure of families which attain this upper bound. A major portion of this dissertation focuses on a recent generalization of the Erdos--Ko--Rado theorem which considers intersecting families of independent sets in graphs. An intersection theorem is proved for a large class of graphs, namely chordal graphs which satisfy an additional condition and similar problems are considered for trees, bipartite graphs and other special classes. A similar extension is also formulated for cross-intersecting families and results are proved for chordal graphs and cycles. A well-known generalization of the EKR theorem for k-wise intersecting families due to Frankl is also considered. A stability version of Frankl's theorem is proved, which provides additional structural information about k-wise intersecting families which have size close to the maximum upper bound. A graph-theoretic generalization of Frankl's theorem is also formulated and proved for perfect matching graphs. Finally, a long-standing conjecture of Chvatal regarding structure of maximum intersecting families in hereditary systems is considered. An intersection theorem is proved for hereditary families which have rank 3 using a powerful tool of Erdos and Rado which is called the Sunflower Lemma. / Dissertation/Thesis / Ph.D. Mathematics 2011

of doctoral thesis Structural graph theory Jan Hladký In the thesis we make progress on the Loebl-Komlós-Sós Conjecture which is a classic problem in the field of Extremal Graph Theory. We prove the following weaker version of the Conjecture: For every α > 0 there exists a number k0 such that for every k > k0 we have that every n-vertex graph G with at least (1 2 +α)n vertices of degrees at least (1+α)k contains each tree T of order k as a subgraph. The proof of our result follows a strategy common to approaches which employ the Szemerédi Regularity Lemma: the graph G is decomposed, a suitable combinatorial structure inside the decomposition is found, and then the tree T is embedded into G using this structure. However the decomposition given by the Regularity Lemma is not of help when G sparse. To surmount this shortcoming we develop a decomposition technique that applies also to sparse graphs: each graph can be decomposed into vertices of huge degrees, regular pairs (in the sense of the Regularity Lemma), and two other components each exhibiting certain expander-like properties. The results were achieved in a joint work with János Komlós, Diana Piguet, Miklós Simonovits, Maya Jakobine Stein and Endre Szemerédi. 1

We give a short and elementary proof of Jung’s theorem, which states that for a field K of characteristic zero the automorphisms of K[x, y] are generated by elementary automorphisms and linear automorphisms. / Presentaremos una prueba corta y elemental del teorema de Jung. Este teorema establece que para un cuerpo K de caracterstica cero los automor smos de K[x; y] son generados por automorsmos lineales y los llamados elementales.

In this thesis we study algorithmic aspects of balanced group presentations which are finite presentations with the same number of generators and relations. The main motivation is that the decidability of some problems, such as the triviality problem, is open for balanced presentations. First, we summarize known results on decision problems for general finite presen- tations and we show two group properties which are undecidable even for balanced presentations - the property of "being a free group"' and the property of "having a finite presentation with 12 generators". We also show reductions of some graph problems to the triviality problem for group presentations, such as determining whether a graph is connected, k-connected or connected including an odd cycle. Then we show a reduction of the determining whether a graph with the same number of vertices and edges is a cycle to the triviality problem for balanced presentations. On the other hand, there is also a limitation of reduction to balanced presentations. We prove that there is no balanced presentation with two generators a, b|ap(m) bq(m) , ar(m) bs(m) for p(m), q(m), r(m), s(m) ∈ Z[m] which describes the trivial group if and only if m is odd. In the last part of this thesis, we describe a relation between group presentations and topology. In addition,...

Submitted by Aelson Maciera (aelsoncm@terra.com.br) on 2018-01-31T17:48:17Z No. of bitstreams: 1 DissDCS.pdf: 770561 bytes, checksum: be9bc14e68967a56c035cb7a1a5557a4 (MD5) / Approved for entry into archive by Ronildo Prado (bco.producao.intelectual@gmail.com) on 2018-01-31T18:57:43Z (GMT) No. of bitstreams: 1 DissDCS.pdf: 770561 bytes, checksum: be9bc14e68967a56c035cb7a1a5557a4 (MD5) / Approved for entry into archive by Ronildo Prado (bco.producao.intelectual@gmail.com) on 2018-01-31T18:57:51Z (GMT) No. of bitstreams: 1 DissDCS.pdf: 770561 bytes, checksum: be9bc14e68967a56c035cb7a1a5557a4 (MD5) / Made available in DSpace on 2018-01-31T18:58:00Z (GMT). No. of bitstreams: 1 DissDCS.pdf: 770561 bytes, checksum: be9bc14e68967a56c035cb7a1a5557a4 (MD5) Previous issue date: 2017-02-16 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / In this work, we present the Conjecture of Brian Hartley and study its validity, i.e, we verify if group identities in the unity group U(FG) make FG satisfy a polynomial identity, where G is a torsion group and F any field. This study will be made first for infinite fields, and next for any field. From this result, will be deduced necessary and suficient conditions in a group G, for the unity group U(FG) satisfy group identities. / Neste trabalho, apresentamos a Conjectura de Brian Hartley e estudamos sua validade, ou seja, verificamos se identidades de grupo no grupo das unidades U(FG) levam FG a satisfazer identidades polinomiais, onde G e um grupo de torçao e F corpo qualquer. Tal estudo sera realizado primeiramente para corpos infinitos, e em seguida para corpos quaisquer. A partir deste resultado, serao deduzidas condicoes necessarias e suficientes em um grupo G, para que o grupo das unidades U(FG) satisfaca identidades de grupo.