O Recuo Brutalista

Em conformidade com a dúvida de seu título, o difundido livro The New Brutalism: Ethic or Aesthetic? de Reyner Banham não é possível explicar o Brutalismo como manifestação artística coesa, dotada de consistência e reprodutibilidade formal. A citação de arquitetos famosos, porém divergentes, parece associar e comparar obras ásperas com a pretensão de reerguer uma arquitetura moderna considerada ascética, monótona e insuficiente e gera um teoricismo da aparência crua e do moralismo dos objetos. Discurso que oculta, ou desvia a atenção do retorno artístico à sublimidade e construção artesanal. O Brutalismo é aceito como evolução natural dos estágios modernos anteriores e sanciona artefatos toscos, pesados e inacabados como se fossem filiados ao processo moderno desinfestado. Esconde contradições e disfarça seu rompimento com o moderno para prolongar a expressão Movimento moderno. Mas o objeto claro, econômico e preciso é repudiado pelo consumidor e, por ser pouco representativo, o artista faz sua maquiagem com episódios contrastantes e monumentais na informalidade das cidades espontâneas. No entanto, parece possível suspender a noção positiva e corretiva do Brutalismo para entendê-lo como um recuo artístico vulgarizador que despreza aperfeiçoamento e afronta a atitude moderna com banalização conceptiva, exagero, figuralidade, musculação estrutural, grandeza tectônica, rudimento e rudeza. Assim, moralismo, retorno rústico e originalidade desqualificam a expressão International Style entendida como a culminação da arquitetura moderna do pós-guerra, ao depreciá-la como decadente, como produto imobiliário, comercial e corporativo a serviço do capital. Essa interpretação desvela uma crítica anti-industrial, portanto antimodernista e diversa da pós-modernidade, porém contestadora e realista para fornecer imagens à cultura e aos insensíveis à estrutura da forma moderna. Diverso da pós-modernidade pela dependência ao moderno e ausência de apelo popular. Tornada insignificante a configuração oportuna do artefato, o arquiteto tenta reter sua notabilidade artística, ou o prestígio que parece enfraquecer na aparência símile da especificação de catálogo, no rigor modular. Indispõe-se e repudia componentes, Standards e acabamentos impessoais da indústria da construção para insistir em autoria e inspiração, mas repete cacoetes estilísticos de época e o inexplicável uso intensivo de concreto bruto e aparente para sentir-se engajado e atualizado. Porém, é necessário distinguir obras de aparência severa concebidas pela atitude moderna mais autêntica das de concreto aparente em tipos ou configurações aberrantes. Para avançar na discussão do Brutalismo propõe-se entender este fenômeno com a substituição do juízo estético moderno de sentido visual postulado por Immanuel Kant (1724-1804) por um sentimento estético fácil e relacionado com a sensação da empatia, com a Einfühlung de Robert Vischer (1847-1933). Na época da cultura de massas, admite-se o rebaixamento das exigências no artefato e a adaptação brutalista com a transfiguração dos processos de arquitetura moderna. Assim, a forma é substituída pela figura ou pelo resumo material; a estrutura formal subjacente pelo ritmo e exposição da estrutura física; o reconhecimento visual pelo entusiasmo psicológico ou pelo impulso dionisíaco; a concepção substituída pelo partido, ou, ainda, pelo conceito; a sistematização e a ordem pela moldagem e a organização; a abstração e síntese pela originalidade e essencialidade, o sentido construtivo pela honestidade material; a identidade das partes pela fundição ou pela unicidade objetal e a residência pela cabana primitiva.

Intersections on moduli spaces of curves

We present a new approach to perform calculations with the certain standard classes in cohomology of the moduli spaces of curves. It is based on an important lemma of Ionel relating the intersection theoriy of the moduli space of curves and that of the space of admissible coverings. As particular results, we obtain expressions of Hurwitz numbers in terms of the intersections in the tautological ring, expressions of the simplest intersection numbers in terms of Hurwitz numbers, an algorithm of calculation of certain correlators which are the subject of the Witten conjecture, an improved algorithm for intersections related to the Boussinesq hierarchy, expressions for the Hodge integrals over two-pointed ramification cycles, cut-and-join type equations for a large class of intersection numbers, etc.

A simple strategy for defining polynomial spline spaces over hierarchical T-meses

[EN]We present a new strategy for constructing spline spaces over hierarchical T-meshes with quad- and octree subdivision scheme. The proposed technique includes some simple rules for inferring local knot vectors to define C 2 -continuous cubic tensor product spline blending functions. Our conjecture is that these rules allow to obtain, for a given T-mesh, a set of linearly independent spline functions with the property that spaces spanned by nested T-meshes are also nested, and therefore, the functions can reproduce cubic polynomials. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0- balanced mesh...

Aspects of Integrability in Gauge/String Correspondence

In this thesis, we present our work about some generalisations of ideas, techniques and physical interpretations typical for integrable models to one of the most outstanding advances in theoretical physics of nowadays: the AdS/CFT correspondences. We have undertaken the problem of testing this conjectured duality under various points of view, but with a clear starting point - the integrability - and with a clear ambitious task in mind: to study the finite-size effects in the energy spectrum of certain string solutions on a side and in the anomalous dimensions of the gauge theory on the other. Of course, the final desire woul be the exact comparison between these two faces of the gauge/string duality. In few words, the original part of this work consists in application of well known integrability technologies, in large parte borrowed by the study of relativistic (1+1)-dimensional integrable quantum field theories, to the highly non-relativisic and much complicated case of the thoeries involved in the recent conjectures of AdS5/CFT4 and AdS4/CFT3 corrspondences. In details, exploiting the spin chain nature of the dilatation operator of N = 4 Super-Yang-Mills theory, we concentrated our attention on one of the most important sector, namely the SL(2) sector - which is also very intersting for the QCD understanding - by formulating a new type of nonlinear integral equation (NLIE) based on a previously guessed asymptotic Bethe Ansatz. The solutions of this Bethe Ansatz are characterised by the length L of the correspondent spin chain and by the number s of its excitations. A NLIE allows one, at least in principle, to make analytical and numerical calculations for arbitrary values of these parameters. The results have been rather exciting. In the important regime of high Lorentz spin, the NLIE clarifies how it reduces to a linear integral equations which governs the subleading order in s, o(s0). This also holds in the regime with L ! 1, L/ ln s finite (long operators case). This region of parameters has been particularly investigated in literature especially because of an intriguing limit into the O(6) sigma model defined on the string side. One of the most powerful methods to keep under control the finite-size spectrum of an integrable relativistic theory is the so called thermodynamic Bethe Ansatz (TBA). We proposed a highly non-trivial generalisation of this technique to the non-relativistic case of AdS5/CFT4 and made the first steps in order to determine its full spectrum - of energies for the AdS side, of anomalous dimensions for the CFT one - at any values of the coupling constant and of the size. At the leading order in the size parameter, the calculation of the finite-size corrections is much simpler and does not necessitate the TBA. It consists in deriving for a nonrelativistc case a method, invented for the first time by L¨uscher to compute the finite-size effects on the mass spectrum of relativisic theories. So, we have formulated a new version of this approach to adapt it to the case of recently found classical string solutions on AdS4 × CP3, inside the new conjecture of an AdS4/CFT3 correspondence. Our results in part confirm the string and algebraic curve calculations, in part are completely new and then could be better understood by the rapidly evolving developments of this extremely exciting research field.

Bistable elliptic equations with fractional diffusion

This work concerns the study of bounded solutions to elliptic nonlinear equations with fractional diffusion. More precisely, the aim of this thesis is to investigate some open questions related to a conjecture of De Giorgi about the one-dimensional symmetry of bounded monotone solutions in all space, at least up to dimension 8. This property on 1-D symmetry of monotone solutions for fractional equations was known in dimension n=2. The question remained open for n>2. In this work we establish new sharp energy estimates and one-dimensional symmetry property in dimension 3 for certain solutions of fractional equations. Moreover we study a particular type of solutions, called saddle-shaped solutions, which are the candidates to be global minimizers not one-dimensional in dimensions bigger or equal than 8. This is an open problem and it is expected to be true from the classical theory of minimal surfaces.

On Sandwiched Singularities

Sandwich-Singularitäten sind die Singularitäten auf derNormalisierung von Aufblasungen eines regulärenFlächenkeimes. In der Arbeit wird ein enger Zusammenhangzwischen Topologie und Deformationstheorie vonSandwich-Singularitäten einerseits und ebenenKurvensingularitäten andererseits dargestellt. NeueErgebnisse betreffen u.a. Deformationen vonnulldimensionalen komplexen Räumen in der Ebene, die durchvollständige Ideale beschrieben werden, z.B. wann'simultanes Aufblasen' der Fasern einer solchen Deformationmöglich ist. Zudem werden Glättungskomponenten und dieKollar-Vermutung für Sandwich-Singularitäten untersucht undim Zusammenhang damit numerische Kriterien für die Frage, obdie symbolische Algebra einer Raumkurve endlich erzeugt ist.

A dictionary of modular threefolds

The thesis deals with the modularity conjecture for three-dimensional Calabi-Yau varieties. This is a generalization of the work of A. Wiles and others on modularity of elliptic curves. Modularity connects the number of points on varieties with coefficients of certain modular forms. In chapter 1 we collect the basics on arithmetic on Calabi-Yau manifolds, including general modularity results and strategies for modularity proofs. In chapters 2, 3, 4 and 5 we investigate examples of modular Calabi-Yau threefolds, including all examples occurring in the literature and many new ones. Double octics, i.e. Double coverings of projective 3-space branched along an octic surface, are studied in detail. In chapter 6 we deal with examples connected with the same modular forms. According to the Tate conjecture there should be correspondences between them. Many correspondences are constructed explicitly. We finish by formulating conjectures on the occurring newforms, especially their levels. In the appendices we compile tables of coefficients of weight 2 and weight 4 newforms and many examples of double octics.

Eduard Study (1862-1930) - ein mathematischer Mephistopheles im geometrischen Gärtchen

Diese Arbeit befasst sich mit Eduard Study (1862-1930), einem der deutschen Geometer um die Jahrhundertwende, der seine Zeit zum Einen durch seine Kontakte zu Klein, Hilbert, Engel, Lie, Gordan, Halphen, Zeuthen, Einstein, Hausdorff und Weyl geprägt hat, zum Anderen in ihr aber auch für seine beißenden und stilistisch ausgefeilten Kritiken ebenso berühmt wie berüchtigt war. Da sich Study mit einer Vielzahl mathematischer Themen beschäftigt hat, führen wir zunächst in die von ihm bearbeiteten Gebiete der Geometrie des 19. Jahrhunderts ein (analytische und synthetische Geometrie im Sinne von Monge, Poncelet, Plücker und Reye, Invariantentheorie Clebsch-Gordan'scher Prägung, abzählende Geometrie von Chasles und Halphen, die Werke Lie's und Grassmann’s, Liniengeometrie sowie Axiomatik und Grundlagenkrise). In seiner darauf folgenden Biographie finden sich als zentrale Stellen seine Habilitation bei Klein über die Chasles’sche Vermutung, sein Streit mit Zeuthen darüber als eine der Debatten der Mathematischen Annalen (aus der er historisch zwar nicht, mathematisch aber tatsächlich als Gewinner hätte herausgehen müssen, wie wir an der Lösung des Problems durch van der Waerden sehen werden) und seine Auseinandersetzungen als etablierter Bonner Professor mit Engel über Lie, Weyl über Invariantentheorie, zahlreichen philosophischen Richtungen über das Raumproblem, Pasch’s Axiomatik, Hilbert’s Formalismus sowie Brouwer’s und Weyl’s Intuitionismus.

Essays on geography and diseases

This dissertation explores how diseases contributed to shape historical institutions and how health and diseases are still affecting modern comparative development. The overarching goal of this investigation is to identify the channels linking geographic suitability to diseases and the emergence of historical and modern insitutions, while tackling the endogenenity problems that traditionally undermine this literature. I attempt to do so by taking advantage of the vast amount of newly available historical data and of the richness of data accessible through the geographic information system (GIS). The first chapter of my thesis, 'Side Effects of Immunities: The African Slave Trade', proposes and test a novel explanation for the origins of slavery in the tropical regions of the Americas. I argue that Africans were especially attractive for employment in tropical areas because they were immune to many of the diseases that were ravaging those regions. In particular, Africans' resistance to malaria increased the profitability of slaves coming from the most malarial parts of Africa. In the second chapter of my thesis, 'Caste Systems and Technology in Pre-Modern Societies', I advance and test the hypothesis that caste systems, generally viewed as a hindrance to social mobility and development, had been comparatively advantageous at an early stage of economic development. In the third chapter, 'Malaria as Determinant of Modern Ethnolinguistic Diversity', I conjecture that in highly malarious areas the necessity to adapt and develop immunities specific to the local disease environment historically reduced mobility and increased isolation, thus leading to the formation of a higher number of different ethnolinguistic groups. In the final chapter, 'Malaria Risk and Civil Violence: A Disaggregated Analysis for Africa', I explore the relationship between malaria and violent conflicts. Using georeferenced data for Africa, the article shows that violent events are more frequent in areas where malaria risk is higher.

Absolute Hodge cycles and Deligne's principle b

I cicli di Hodge assoluti sono stati utilizzati da Deligne per dividere la congettura di Hodge in due sotto-congetture. La prima dice che tutte le classi di Hodge su una varietà complessa proiettiva liscia sono assolute, la seconda che le classi assolute sono algebriche. Deligne ha dato risposta affermativa alla prima sottocongettura nel caso delle varietà abeliane. La dimostrazione si basa su due teoremi, conosciuti rispettivamente come Principio A e Principio B. In questo lavoro vengono presentate la teoria delle classi di Hodge assolute e la dimostrazione del Principio B.

Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory.rnAs its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained.rnThe constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point.rnFinally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of existing computations, taking the independent running of the Euler topological term into account. Known perturbative results are reproduced in this case from the renormalization group equation, identifying however a unique non-Gaussian fixed point.rn

Monodromy calculations for some differential equations

In vielen Teilgebieten der Mathematik ist es w"{u}nschenswert, die Monodromiegruppe einer homogenen linearen Differenzialgleichung zu verstehen. Es sind nur wenige analytische Methoden zur Berechnung dieser Gruppe bekannt, daher entwickeln wir im ersten Teil dieser Arbeit eine numerische Methode zur Approximation ihrer Erzeuger.rnIm zweiten Abschnitt fassen wir die Grundlagen der Theorie der Uniformisierung Riemannscher Fl"achen und die der arithmetischen Fuchsschen Gruppen zusammen. Auss erdem erkl"aren wir, wie unsere numerische Methode bei der Bestimmung von uniformisierenden Differenzialgleichungen dienlich sein kann. F"ur arithmetische Fuchssche Gruppen mit zwei Erzeugern erhalten wir lokale Daten und freie Parameter von Lam'{e} Gleichungen, welche die zugeh"origen Riemannschen Fl"achen uniformisieren. rnIm dritten Teil geben wir einen kurzen Abriss zur homologischen Spiegelsymmetrie und f"uhren die $widehat{Gamma}$-Klasse ein. Wir erkl"aren wie diese genutzt werden kann, um eine Hodge-theoretische Version der Spiegelsymmetrie f"ur torische Varit"aten zu beweisen. Daraus gewinnen wir Vermutungen "uber die Monodromiegruppe $M$ von Picard-Fuchs Gleichungen von gewissen Familien $f:mathcal{X}rightarrow bbp^1$ von $n$-dimensionalen Calabi-Yau Variet"aten. Diese besagen erstens, dass bez"uglich einer nat"urlichen Basis die Monodromiematrizen in $M$ Eintr"age aus dem K"orper $bbq(zeta(2j+1)/(2 pi i)^{2j+1},j=1,ldots,lfloor (n-1)/2 rfloor)$ haben. Und zweitens, dass sich topologische Invarianten des Spiegelpartners einer generischen Faser von $f:mathcal{X}rightarrow bbp^1$ aus einem speziellen Element von $M$ rekonstruieren lassen. Schliess lich benutzen wir die im ersten Teil entwickelten Methoden zur Verifizierung dieser Vermutungen, vornehmlich in Hinblick auf Dimension drei. Dar"uber hinaus erstellen wir eine Liste von Kandidaten topologischer Invarianten von vermutlich existierenden dreidimensionalen Calabi-Yau Variet"aten mit $h^{1,1}=1$.

Hearing Delzant Polytopes From the Equivariant Spectrum

Let M^{2n} be a symplectic toric manifold with a fixed T^n-action and with a toric K\"ahler metric g. Abreu asked whether the spectrum of the Laplace operator $\Delta_g$ on $\mathcal{C}^\infty(M)$ determines the moment polytope of M, and hence by Delzant's theorem determines M up to symplectomorphism. We report on some progress made on an equivariant version of this conjecture. If the moment polygon of M^4 is generic and does not have too many pairs of parallel sides, the so-called equivariant spectrum of M and the spectrum of its associated real manifold M_R determine its polygon, up to translation and a small number of choices. For M of arbitrary even dimension and with integer cohomology class, the equivariant spectrum of the Laplacian acting on sections of a naturally associated line bundle determines the moment polytope of M.

The Fundamental Gap For Hyperbolic Triangles

In 1983, M. van den Berg made his Fundamental Gap Conjecture about the difference between the first two Dirichlet eigenvalues (the fundamental gap) of any convex domain in the Euclidean plane. Recently, progress has been made in the case where the domains are polygons and, in particular, triangles. We examine the conjecture for triangles in hyperbolic geometry, though we seek an for an upper bound for the fundamental gap rather than a lower bound.

Comparing skew Schur functions: a quasisymmetric perspective

Reiner, Shaw and van Willigenburg showed that if two skew Schur functions sA and sB are equal, then the skew shapes $A$ and $B$ must have the same "row overlap partitions." Here we show that these row overlap equalities are also implied by a much weaker condition than Schur equality: that sA and sB have the same support when expanded in the fundamental quasisymmetric basis F. Surprisingly, there is significant evidence supporting a conjecture that the converse is also true. In fact, we work in terms of inequalities, showing that if the F-support of sA contains that of sB, then the row overlap partitions of A are dominated by those of B, and again conjecture that the converse also holds. Our evidence in favor of these conjectures includes their consistency with a complete determination of all F-support containment relations for F-multiplicity-free skew Schur functions. We conclude with a consideration of how some other quasisymmetric bases fit into our framework.