19 research outputs found

    Celebrated Econometricians: Katarina Juselius and Søren Johansen

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    This Special Issue collects contributions related to advances in the theory and practice of Econometrics induced by the research of Katarina Juselius and Søren Johansen, whom this Special Issue aims to celebrate. The papers in this Special Issue provide advances on several topics, and they are grouped in the following areas, with three to four papers per group). The first group provides a historical perspective on Katarina’s and Søren’s contributions to Econometrics. The second group of papers concentrates on representation theory, while the third focuses on estimation and inference. The fourth group explores extensions of CVARs for modelling and forecasting, and the fifth and final group is centered on empirical applications

    Quaternion Algebras

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    This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout

    Generalized averaged Gaussian quadrature and applications

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    A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

    MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

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    Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

    Sur le second théorème principal

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    Kobayashi's conjecture asserts that a generic hypersurface X in CPn+1 having degree d>= 2n+1 is complex hyperbolic, a problem that has attracted much attention recently, also with the hope of setting up a complete higher dimensional Nevanlinna theory.In the first part of this thesis, our goal is to construct examples of hyperbolic hypersurfaces in projective spaces of degree as low as possible. First of all, taking into account the truncation level in Cartan's Second Main Theorem, we establish the hyperbolicity of complements of some configurations of hyperplanes with passage points, extending a classical result of Bloch-Fujimoto-Green. This allows us to launch a recent algorithm of Duval, based on the deformation method of Zaidenberg, on creating hyperbolic sextics in CP3, hence to construct families of hyperbolic hypersurfaces X in CPn+1 having degree d=2n+2 for 2=((n+3)/2)^2 in CPn+1.In the second part, we study the problem of decreasing the truncation level in Cartan's Second Main Theorem. It was conjectured by Noguchi that in this theorem, for a family of 4 lines in general position in CP2, if an entire holomorphic curve from C to CP2 is assumed to be algebraically nondegenerate, then the truncation level can be decreased to 1. Using Ahlfors'theory of covering surfaces, we propose a positive answer in the case where the curve f is close to some algebraic curve c in CP2, in the sense that the set of accumulation points of f(C) at infinity, the cluster set of f is contained in c.La conjecture de Kobayashi stipule qu'une hypersurface générique X dans CPn+1de degré d>= 2n+1 esthyperbolique complexe, un problème qui a attiré une grande attention récemment, avec l'espoir de mettre au point une théorie de Nevanlinna complète en dimension supérieure.Dans la première partie de cette thèse, notre objectif est de construire des exemples d'hypersurfaces hyperboliques de l'espace projectif dont le degré soit aussi petit que possible. Tout d'abord, en tenant compte du niveau de troncation dans le Second Théorème Principal de Cartan, nous établissons l'hyperbolicité de complémentaires de certaines configurations d'hyperplans avec points de passages, ce qui étend un résultat classique de Bloch-Fujimoto-Green. Ceci nous permet d'amorcer un algorithme récent de Duval, basé sur la méthode de déformation de Zaidenberg, pour créer des sextiques hyperboliques dans CP3, et de construire ainsi des familles d'hypersurfaces hyperboliques X dans CPn+1 de degré =2n+2 pour 2=((n+3)/2)^2 dans CPn+1.Dans la deuxième partie, nous étudions le problème de diminuer le niveau de troncation dans le Second Théorème Principal de Cartan. Noguchi a conjecturé que dans ce théorème, pour une famille de 4 droites en position générale dans CP2, si une courbe holomorphe entière f de C dans CP2 est supposée n'être pas algébriquement dégénérée, alors le niveau de troncation peut être abaissé à 1. En utilisation la théorie de recouvrement d'Ahlfors pour les surfaces, nous proposons une réponse positive dans le cas où la courbe f est proche d'une certaine courbe algébrique c dans CP2, au sens où l'ensemble d'accumulation de f(C) à l'infini, le cluster set de f est contenu dans c

    Quanta of Maths

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    The work of Alain Connes has cut a wide swath across several areas of math- ematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics
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