This report proposes that the architectural structure of Italo Calvino’s novel If on a Winter’s Night a Traveler evolved from the writer’s personal experience engaging with the figurative arts through ekphrastic writing, namely the essays he composed for the art of Saul Steinberg. This argument contributes to the promising discourse of how these two artist-writers blurred the divisions between figurative arts and creative writing, each in his own right, by exploring the visual themes of the narrated, and the narrative themes of the visual. Examination is focused on selected Steinberg pieces that represent Steinbergian themes, the Calvino essays for Saul Steinberg, and on a combination of extant art criticism and academic scholarship. The goal of this work is to demonstrate that through their mutual transposition of words and images, each artist-writer illuminates the work of the other. / text

My dissertation investigates questions of boredom and architecture in the middle decades of the twentieth century through the work of two figures: the American-Italian architect Robert Venturi (b. 1925) and the Romanian-born American architect and artist Saul Steinberg (1914-1999). The topic of boredom in architecture, and specifically within this timeframe, has been largely ignored in architectural history, theory, and criticism where, with the exception of a few articles, there is no consistent body of scholarship on this issue. Looming large in the sterile iterations of various –isms, boredom remains critical in contemporary architectural practice as the production and obsolescence of images becomes ever faster with new technologies. Quickly saturated with information presented in fleeting displays that are easy to produce, easy to delete, and easy to consume, as soon as our expectation for novelty and change fails to satisfy us, we fall back into the loop of boredom. While boredom as the dissociation of person from place has raised architects' interest especially during the middle decades of the twentieth century, there is no significant scholarship on this topic. In this context, my research looks at the work of two architects who go beyond the attractive rhetoric of boredom and explore its potential as both a critical and a generative tool. / PHD

A graph is (t+1)-critical if it is not t-colorable, but every proper subgraph is. In this thesis, we study the structure of critical graphs on higher surfaces. One major result in this area is Carsten Thomassen's proof that there are finitely many 6-critical graphs on a fixed surface. This proof involves a structural theorem about a precolored cycle C of length q. In general terms, he proves that a coloring, c, of C, can be extended inside the cycle, or there exists a subgraph H with at most a number of vertices exponential in q such that c can not be extended to a 5-coloring of H. In Chapter 2, we proved an alternative proof that reduces the number of vertices in H to be cubic in q. In Chapter 3, we find the nine 6-critical graphs among all graphs embeddable on the Klein bottle. In Chapter 4, we prove a result concerning critical graphs related to an analogue of Steinberg's conjecture for higher surfaces. We show that if G is a 4-critical graph embedded on surface S, with Euler genus g and has no cycles of length four through ten, then G has at most 2442g + 37 vertices.

Thesis (MPhil)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: This study attempts to explore aspects of the textual representation of Magadien Wentzel, the main character of The Number, a work of literary journalism by Jonny Steinberg. It sets out to respond to the following two central research questions: Firstly, what narrative decisions does Jonny Steinberg make in the text of The Number to convey aspects of the reality he experienced in relation to his main character, Magadien Wentzel; and secondly, what effect do these decisions have on the reader? As literary journalism is a genre with fluid boundaries and therefore various definitions, the thesis first presents the challenge of definition and lays out a broad history of the genre in its attempt to situate The Number as a work of social documentary and of literary journalism in South Africa. Taking realism as its theoretical point of departure, this study aligns itself with the view that there exists an independent, extra-textual real-world and that knowledge of this real-world can be produced and shared. In doing so, realism presents itself as a literary form associated with art that cannot turn away from harsh aspects of human existence – a characteristic mirrored by Steinberg’s (and thus his character’s) major themes. By means of a textual analysis which seeks to interpret aspects of Steinberg’s narrative decisions in his text, this study uses tools of literary realism, namely the empirical effect and the character effect, in its exploration. This research, conducted within the qualitative research paradigm, is informed in particular by the assumption that there exists an implicit communicative contract between author and reader which leads to narrative trust, seen as an indispensable quality to the non-fictional reading experience. In the case of Steinberg and The Number, this study finds that the writer’s representation of a particular reality relies to an important degree on the level of trust he is able to inspire in a reader. This is pertinent because, being factual, non-fiction demands that a reader not only imagine a world other than their own, but that they believe it too. One of the ways in which Steinberg enables a reader to trust his representation of his particular reality is by overtly placing his literary and authorial concerns alongside his reportage of Magadien Wentzel, the main character of The Number. This distinctive narrative approach results in a modification of the reader’s traditional contract with the writer, forged by the text between them, to one in which the text unites the reader with both Steinberg as narrator and Magadien Wentzel as character. / AFRIKAANSE OPSOMMING: Hierdie studie poog om aspekte van die tekstuele voorstelling van Magadien Wentzel, die hoofkarakter in The Number, 'n werk van literêre joernalistiek deur Jonny Steinberg, te verken. Dit probeer om die volgende twee sentrale navorsingsvrae te beantwoord: Eerstens, watter narratiewe besluite neem Jonny Steinberg in die teks van The Number om aspekte van die werklikheid wat hy ervaar het met betrekking tot sy hoofkarakter, Magadien Wentzel, oor te dra, en tweedens, watter effek het dit op die leser? Aangesien literêre joernalistiek 'n genre is met vloeibare grense en daarom verskeie definisies, probeer die tesis eerstens die uitdaging van definisie te beantwoord. Daarmee lê dit ook 'n breë basis van die geskiedenis van die genre in sy poging om The Number te situeer as 'n sosiale dokumentêr en as literêre joernalistiek in Suid-Afrika. Met realisme as teoretiese vertrekpunt, vereenselwig hierdie studie hom daarmee dat 'n onafhanklike, ekstra-tekstuele regte wêreld bestaan, en dat kennis van dié “regte wêreld” geskep en gedeel kan word. So representeer realisme hom as 'n literêre vorm wat verband hou met die kunste, en wat sigself nie kan afwend van die harde aspekte van die menslike bestaan nie – 'n kenmerk wat deur Steinberg se hooftemas – en daarom ook dié van sy hoofkarakter – weerspieël word. Deur middel van 'n tekstuele analise wat poog om aspekte van Steinberg se narratiewe besluite in sy teks te interpreteer, gebruik hierdie studie aspekte van literêre realisme, naamlik die empiriese effek en die karakter-effek, in sy ondersoek. Hierdie navorsing, wat binne die kwalitatiewe navorsingsparadigma uitgevoer is, is veral geïnformeer deur die aanname dat daar 'n implisiete kommunikatiewe kontrak tussen die skrywer en die leser bestaan wat lei tot narratiewe vertroue, gesien as 'n onmisbare element van die nie-fiksie-leeservaring. In die geval van Steinberg en The Number het hierdie studie bevind dat die skrywer se voorstelling van 'n bepaalde werklikheid tot 'n belangrike mate berus op die vlak van vertroue wat hy by die leser genereer. Dit is belangrik, want synde feitelik, vereis nie-fiksie dat 'n leser nie net 'n wêreld anders as hul eie voorstel nie, maar dat hulle ook daarin kan glo. Een van die maniere waarop Steinberg 'n leser in staat stel om sy voorstelling van sy besondere werklikheid te vertrou, is deur die plasing van sy literêre en outeursbesorgdheid direk langs sy reportage van Magadien Wentzel, die hoofkarakter in The Number. Hierdie unieke narratiewe aanslag het ’n modifikasie van die leser se tradisionele kontrak met die skrywer tot gevolg, ’n kontrak wat gewoonlik deur die teks tussen hulle gesmee is, en wat verander in een waarin die teks die leser met beide Steinberg as verteller en Magadien Wentzel as karakter verenig het.

Dans son preprint, M. Bruno Kahn a construit une suite spectrale par rang en utilisant la méthode catégorique. Cette suite spectrale est construit par une filtration de la catégorie des modules sans-torsion de type fini d'un anneau intègre A ce qui explique le nom : suite spectrale par rangs. Cette suite spectrale converge vers les groupes d'homologies de la Q-construction de la catégorie de A-modules sans torsion de type fini et elle été utilisé par Quillen pour prouver que les K-groupes sont de génération finie pour anneau d'intègres d'un corps de nombres. Notre but de cette thèse est de calculer le différentiel de la suite spectrale par rangs qui peut servit comme une première étape d'une idée générale d'unifier les calculs de rangs des K-groupes de la courbe sur un corps fini (G. Harder) et la courbe arithmétique (A. Borel). Pour gagner ça, nous étudions le foncteur cellulaire (connexe) et les constructions de Grothendieck en détail, en particulier ses propriétés homotopiques. En utilisant ça, nous pouvons mettre le différentiel dans certain triangles distingués de foncteurs sur une catégorie, puis nous réalisons ces foncteurs explicits en langages d'immeuble de Tits, module de Steinberg et symbole modulaire au sens d'Ash-Rudolph. Nous avons aussi obliger de fabriquer un autre symbole : le symbole étendu pour étudier l'homologie de la suspension d'immeuble de Tits, mais nous montons que ce symbole est équivalent que symbole modulaire. / Bruno Kahn has constructed a rank spectral sequence by using a purely categorical approach. This spectral sequence was derived by using a filtration of the category of torsion-free modules over integral domain by ranks and hence the name: rank spectral sequence. This spectral sequence converges to the homology groups of the Q-construction over the category of finitely generated torsion-free modules over an integral ring. Quillen used it in the proof of the finite generation of K-groups of rings of integers. Our goal in this thesis is to calculate the differential of the rank spectral sequence. We believe that this is a first step towards a much bigger project, that is, to unify the calculation of the ranks of K-groups of curves over a finite field (result of G. Harder) and of arithmetic curves (result of A. Borel).To achieve our goal, we put the differential in certain distinguished triangles of coefficients/functors over some categories, and make these functors explicit in terms of Tits building and Ash-Rudolph's modular symbols. To accomplish this, we shall use Quillen's categorical homotopy theory intensively and introduce the notion of extended (modular) symbols which is equivalent to Ash-Rudolph's via the suspension of Tits buildings.

A pesquisa é voltada para o estudo da obra de Saul Steinberg, com enfoque nas contribuições de sua produção para o desenvolvimento do cartum moderno e das artes gráficas. Para tanto, busca sistematizar a vida e obra de Steinberg (1914-1999), com ênfase nas transformações ocorridas em seu trabalho no decorrer de sua carreira, relacionando-as ao conjunto de sua produção, ao contexto histórico e à produção das artes gráficas - cartum, ilustração, desenho gráfico. O trabalho busca desenvolver uma análise do desenho do artista, partindo da hipótese de seu caráter moderno - baseado em síntese e simplicidade. É intenção desta pesquisa, também, contribuir com o mapeamento de parte da história das artes gráficas do Brasil e do mundo, neste caso privilegiando a produção gráfica moderna do século XX. / The research deals with the study of the work of Saul Steinberg, with focus in the contributions of his work to the development of the modern cartoon and graphic arts. It tries to systematize the life and work of Steinberg (1914-1999), with emphasis in the transformations occured in his work, related to his whole production, to the historial context, and to the production of the graphic arts. The research tries to develop an analysis of the Steinberg´s drawing, taking into consideration the hypothesis of its modern particularity - established in synthesis and simplicity. Is an intention of this research to contribute with the mapping of part of the graphic art history of Brazil and the world, focusing in the graphic modern production of the 20th century.

A pesquisa é voltada para o estudo da obra de Saul Steinberg, com enfoque nas contribuições de sua produção para o desenvolvimento do cartum moderno e das artes gráficas. Para tanto, busca sistematizar a vida e obra de Steinberg (1914-1999), com ênfase nas transformações ocorridas em seu trabalho no decorrer de sua carreira, relacionando-as ao conjunto de sua produção, ao contexto histórico e à produção das artes gráficas - cartum, ilustração, desenho gráfico. O trabalho busca desenvolver uma análise do desenho do artista, partindo da hipótese de seu caráter moderno - baseado em síntese e simplicidade. É intenção desta pesquisa, também, contribuir com o mapeamento de parte da história das artes gráficas do Brasil e do mundo, neste caso privilegiando a produção gráfica moderna do século XX. / The research deals with the study of the work of Saul Steinberg, with focus in the contributions of his work to the development of the modern cartoon and graphic arts. It tries to systematize the life and work of Steinberg (1914-1999), with emphasis in the transformations occured in his work, related to his whole production, to the historial context, and to the production of the graphic arts. The research tries to develop an analysis of the Steinberg´s drawing, taking into consideration the hypothesis of its modern particularity - established in synthesis and simplicity. Is an intention of this research to contribute with the mapping of part of the graphic art history of Brazil and the world, focusing in the graphic modern production of the 20th century.

Cette thèse est consacrée à deux aspects du programme de Langlands local p-adique et de la compatibilité local-global p-adique.Dans la première partie, j'étudie la question de savoir comment extraire, d'un certain sous-espace Hecke-isotypique de formes automorphes modulo p, suffisament d'invariants d'une représentation galoisienne. Soient p un nombre premier, n>2 un entier, et F un corps à multiplication complexe dans lequel p est complètement décomposé. Supposons qu'une représentation galoisienne automorphe continue r-:Gal(Q-/F)→GLn(F-p) est triangulaire supérieure et suffisament générique ( dans un certain sens ) en une place w au-dessus de p. On montre, en admettant un résultat d'élimination de poids de Serre prouvé dans [LLMPQ], que la classe d'isomorphisme de r-|_Gal(Q-p/Fw) est déterminée par l'action de GLn(Fw) sur un espace de formes automorphes modulo p découpé par l'idéal maximal associée à r- dans une algèbre de Hecke. En particulier, on montre que la partie sauvagement ramifiée de r-|_Gal(Q-p/Fw) est déterminée par l'action de sommes de Jacobi ( vus comme éléments de Fp[GLn(Fp)] ) sur cet espace.La deuxième partie de ma thèse vise à établir une relation entre les résultats précédents de [Schr11], [Bre17] and [BD18]. Soient E une extension finie de Qp suffisamment grande et ρp: Gal(Q-p/Qp)→GL3(E) une représentation p-adique semi-stable telle que la représentation de Weil-Deligne WD(ρp) associée a un opérateur de monodromie N de rang 2 et que la filtration de Hodge associée est non-critique. On sait que la filtration de Hodge de ρp dépend de trois invariants dans E. On construit une famille de représentations localement analytiques Σ^min(λ, L1, L2, L3) qui dépend de trois invariants L1, L2, L3 dans E et telle que chaque représentation contient la représentation localement algébrique Algotimes Steinberg déterminée par ρp. Quand ρp provient, pour un groupe unitaire convenable G/Q, d'une représentation automorphe π de G(A_Q) avec un niveau fixé U^p premier avec p, on montre ( sous quelques hypothèses techniques ) qu'il existe une unique représentation localement analytique dans la famille ci-dessus qui est une sous-représentation du sous-espace Hecke-isotypique associé dans la cohomologie complétée de niveau U^p. On rappelle que [Bre17] a construit une famille de représentations localement analytiques qui dépend de quatre invariants (voir (4) dans [Bre17]) avec une propriété similaire. On donne un critère purement de théorie de représentation: si une représentation Π dans la famille de Breuil se plonge dans un certain sous-espace Hecke-isotypique de la cohomologie complétée, alors elle se plonge nécessairement dans une Σ^min(λ, L1, L2, L3) pour certains choix de L1, L2, L3 dans E qui sont déterminés explicitement par Π. De plus, certains sous-quotients naturels de Σ^min(λ, L1, L2, L3) permettent de construite un complexe de représentations localement analytiques qui "réalise" l'objet dérivé abstrait Σ(λ, underline{L}) defini dans [Schr11]. / This thesis is devoted to two aspects of the p-adic local Langlands program and p-adic local-global compatibility.In the first part, I study the problem of how to capture enough invariants of a local Galois representation from a certain Hecke-isotypic subspace of mod p automorphic forms. Let p be a prime number, n>2 an integer, and F a CM field in which p splits completely. Assume that a continuous automorphic Galois representation r-:Gal(Q-/F)→GLn(F-p) is upper-triangular and satisfies certain genericity conditions at a place w above p, and that every subquotient of r-|_Gal(Q-p/Fw) of dimension >2 is Fontaine-Laffaille generic. We show that the isomorphism class of r-|_Gal(Q-p/Fw) is determined by GLn(Fw)-action on a space of mod p algebraic automorphic forms cut out by the maximal ideal of a Hecke algebra associated to r-, assuming a weight elimination result which is now a theorem to appear in [LLMPQ]. In particular, we show that the wildly ramified part of r-|_Gal(Q-p/Fw) is determined by the action of Jacobi sum operators ( seen as elements of Fp[GLn(Fp)] ) on this space.The second part of my thesis aims at clarifying the relation between previous results in [Schr11], [Bre17] and [BD18]. Let E be a sufficiently large finite extension of Qp and ρp be a p-adic semi-stable representation Gal(Q-p/Qp)→GL3(E) such that the Weil-Deligne representation WD(ρp) associated with it has rank two monodromy operator N and the Hodge filtration associated with it is non-critical. We know that the Hodge filtration of ρp depends on three invariants in E. We construct a family of locally analytic representations Σ^min(λ, L1, L2, L3) of GL3(Qp) depending on three invariants L1, L2, L3 in E with each of the representation containing the locally algebraic representation Algotimes Steinberg determined by ρp. When ρp comes from an automorphic representation π of G(A_Q) with a fixed level U^p prime to p for a suitable unitary group G/Q, we show ( under some technical assumption ) that there is a unique locally analytic representation in the above family that occurs as a subrepresentation of the associated Hecke-isotypic subspace in the completed cohomology with level U^p. We recall that [Bre17] constructed a family of locally analytic representations depending on four invariants ( cf. (4) in [Bre17] ) with a similar property. We give a purely representation theoretic criterion: if a representation Π in Breuil's family embeds into a certain Hecke-isotypic subspace of completed cohomology, then it must equally embed into Σ^min(λ, L1, L2, L3) for certain choices of L1, L2, L3 in E determined explicitly by Π. Moreover, certain natural subquotients of Σ^min(λ, L1, L2, L3) give a true complex of locally analytic representations that realizes the derived object Σ(λ, underline{L}) [Schr11]. Consequently, the family of locally analytic representations Σ^min(λ, L1, L2, L3) give a relation between the higher L-invariants studied in [Bre17] as well as [BD18] and the p-adic dilogarithm function which appears in the construction of Σ^min(λ, L1, L2, L3) in [Schr11].

Dans cette thèse on s'intéresse à la correspondance de Howe géométrique pour les paires duales réductives de type II (G = GL_n, H = GL_m) sur un corps local non-Archimédien F de caractéristique différente de 2, ainsi qu'à la fonctorialité de Langlands géométrique au niveau Iwahori. Notons S la représentation de Weil de G(F) × H(F) et I_H, I_G des sous groupes d'Iwahori de H(F) et G(F). On considère la version géométrique de la représentation S^(I_G×I_H) des algèbres de Hecke-Iwahori H_H et H_G sur laquelle agissent les foncteurs de Hecke. On obtient des résultats partiels sur la description géométrique de la catégorie correspondante. Nous proposons une conjecture décrivant le groupe de Grothendieck de cette catégorie comme module sur les algèbres de Hecke affines étendues de G et de H. Notre description est en termes d'un champ attaché aux groupes de Langlands duaux dans le style de l'isomorphisme de Kazhdan-Lusztig. On démontre cette conjecture pour toutes les paires (GL_1, GL_m). Plus généralement, étant donné deux groupes réductifs connexes G et H et un morphisme \check{G}× SL_2 \to \check{H} de groupes de Langlands duaux, on suggère un bimodule sur les algèbres de Hecke affines étendues de G et de H qui pourrait conjecturalement réaliser la fonctorialité de Langlands géométrique locale au niveau Iwahori.

Ce travail de thèse a pour but de construire et d’étudier une fibration de Hitchin pour les groupes qui apparaît naturellement lorsque l’on essaie de géométriser la formule des traces. On commence par construire une telle fibration en utilisant le semi-groupe de Vinberg. Sur ce semi-groupe de Vinberg, on montre qu’il existe un certain morphisme « polynôme caractéristique » muni d’une section naturelle, de même que dans le cas des algèbres de Lie. On montre également que l’on peut construire un centralisateur régulier au-dessus de cette base des polynômes caractéristiques qui est un schéma en groupes commutatif et lisse.On s’intéresse alors à des variantes pour les groupes des fibres de Springer affines pour lesquelles on remarque que l’introduction du semi-groupe de Vinberg permet d’obtenir une condition d’intégralité analogue à celle de Kazhdan-Lusztig. Ces fibres de Springer affines sont des analogues locaux des fibres de Hitchin. On obtient alors une formule de dimension pour ces fibres.Dans un troisième temps, on s’intéresse à l’aspect global de cette fibration pour laquelle on donne une interprétation modulaire et sur laquelle on construit l’action d’un champ de Picard, issu du centralisateur régulier. L’espace total de cette fibration étant en général singulier, nous étudions son complexe d’intersection. Cet espace de Hitchin s’obtient naturellement comme l’intersection du champ de Hecke avec la diagonale du champ des G-torseurs et on démontre que sur un ouvert suffisamment gros de la base de Hitchin, le complexe d’intersection de l’espace de Hitchin s’obtient par restriction de celui du champ de Hecke corrrespondant.Enfin, dans la dernière partie de cette thèse, on établit un théorème du support dans le cas où l’espace total est singulier analogue à celui de Ngô et l’on démontre que, dans le cas de la fibration de Hitchin, les supports qui interviennent sont reliés aux strates endoscopiques. / This main goal of this work is to construct and study the properties of Hitchin fibration for groups which appears naturally when we try to geometrize the trace formula. We begin by constructing this fibration using the Vinberg’s semigroup. On this semigroup, we show that there exists a characteristic polynomial morphism equipped with a natural section, analog at the Kostant’s one in the case of Lie algebras. We also show that there exists on the base of characteristic polynomials a regular centralizer scheme, which is a smooth commutative group scheme.Then, we are interested in some variant of affine Springer fibers, for which we see that the Vinberg’s semigroup appears naturally to obtain an integrality condition analog to Kazhdan-Lusztig’s one. These affine Springer fibers are local incarnation of Hitchin fibers.In a third time, we go back to the global case and give a modular interpretation of this new Hitchin fibration on which we construct an action of a Picard stack, coming from the regular centralizer.The total space of this fibration, even on the generically regular semisimple locus will be singular and we want to understand his intersection complex. This space can be obtained as the intersection of the Hecke stack with the diagonal of the stack of G-bundles and we show that on a sufficiently big open subset of the Hitchin base, the intersection complex of the Hitchin’s space is the restriction of the corresponding intersection complex on the Hecke stack.Finally, in the last part of this work, we establish a support theorem in the case of a singular total space, generalizing Ngo’s theorem et we show that in the case of Hitchin fibration, the supports that appear are related to the endoscopic strata.