ISBN 978-3-03719-007-4
December 2010, 346 pages, hardcover, 17 x 24 cm.
Fascinating and surprising developments are taking place in the classification of algebraic varieties. Work of Hacon and McKernan and many others is causing a wave of breakthroughs in the Minimal Model Program: we now know that for a smooth projective variety the canonical ring is finitely generated. These new results and methods are reshaping the field.
Inspired by this exciting progress, the editors organized a meeting at Schiermonnikoog and invited leading experts to write papers about the recent developments. The result is the present volume, a lively testimony of the sudden advances that originate from these new ideas.
This volume will be of interest to a wide range of pure mathematicians, but will appeal especially to algebraic and analytic geometers.
Memoires de la SMF 119 (2009), 102 pages
ISBN : 978-2-85629-297-6
Principes d'incertitude associes a des formes quadratiques non degenerees
Ce volume est consacre a des generalisations du principe d'incertitude classique de Hardy dans les espaces Euclidiens. Au lieu de comparer les fonctions a des gaussiennes, nous les comparons a l'exponentielle de formes quadratiques non degenerees, par exemple a la forme de Lorentz. Nous transformons ces problemes a l'aide de la transformee de Bargmann, en des problemes de description de certaines classes de fonctions entieres de plusieurs variables. Ces methode ameliorent et simplifient des resultats publies dans des travaux precedents.
Mots-clefs : Transformees de Fourier, principes d'incertitude, cone de Lorentz, transformee de Bargmann, espace de Fock, transformee de Cayley, distribution temperee
This volume is devoted to several generalisations of the classical Hardy uncertainty principle on Euclidian spaces. Instead of comparing functions and their Fourier transforms a Gaussian, we compare them to the exponential of general non-degenrate quadratic forms, like for example the Lorentz form. Using the Bargmann transform, we translate the problem into the description of several classe of analytic functions of several variables, and at the same time simplify and unify proofs of results presented in several previous papers.
Keywords: Fourier Transforms, uncertainty principles, Lorentz cone, Bargmann transform, Fock space, Cayley transform, tempered distribution
Memoires de la SMF 120
(2010), 120 pages
ISBN : 978-2-85629-296-9
On interprete la theorie des polygones de Harder-Narasimhan par le langage des -filtrations. En utilisant une variante du lemme de Fekete et un argument combinatoire des monomes, on etablit la convergence uniforme des polygones associes a une algebre graduee munie de filtrations. Cela conduit a l'existence de plusieurs invariants arithmetiques dont un cas tres particulier est la capacite sectionnelle. Deux applications de ce resultat en geometrie d'Arakelov sont abordees : le theoreme de Hilbert-Samuel arithmetique ainsi que l'existence et l'interpretation geometrique de la pente maximale asymptotique.
Mots-clefs : Geometrie d'Arakelov, methode de pentes, filtration, polygone de Harder-Narasimhan, theoreme de Hilbert-Samuel
Convergence of Harder-Narasimhan polygons
We interpret the theory of Harder-Narasimhan polygons by the language of -filtrations. By using a variant version of Fekete's lemma and a combinatoric argument on monomials, we establish the uniform convergence of polygons associated to a graded algebra equipped with filtrations. This leads to the existence of several arithmetic invariants a very particular case of which is the sectional capacity. Two applications in Arakelov geometry are developed: the arithmetic Hilbert-Samuel theorem and the existence and the geometric interpretation of the asymptotic maximal slope.
Keywords: Arakelov geometry, slope method, filtration, Harder-Narasimhan polygon, Hilbert-Samuel theorem
Memoires de la SMF 121
(2010), ii+139 pages
ISBN : 978-85629-301-0
Un domaine fondamental pour
Nous decrivons un domaine fondamental pour la surface de Riemann qui parametrise (a conjugaison pres) l'ensemble des fonctions rationelles par le biais des points critiques enumeres, de maniere a ce que le premier point critique ait une periode de 3, et que le deuxieme point critique ne soit pas envoye sur le premier apres iterations ou moins. Cela nous fournit une description, a conjugaison topologique pres, des dynamiques de toutes les composantes de type III en , et nous donne des indications sur un modele topologique de , au meme temps que l'ensemble des composantes hyperboliques qui y sont contenues.
We describe a fundamental domain for the punctured Riemann surface which parametrises (up to Mobius conjugacy) the set of quadratic rational maps with numbered critical points, such that the first critical point has period three, and such that the second critical point is not mapped in iterates or less to the periodic orbit of the first. This gives, in turn, a description, up to topological conjugacy, of all dynamics in all type III hyperbolic components in , and gives indications of a topological model for , together with the hyperbolic components contained in it.
ISBN: 978-1-1180-1064-8
Hardcover
240 pages
April 2011
This book explores the many provocative questions concerning the fundamentals of data analysis. It is based on the time-tested experience of one of the gurus of the subject matter. Why should one study data analysis? How should it be taught? What techniques work best, and for whom? How valid are the results? How much data should be tested? Which machine languages should be used, if used at all? Emphasis on apprenticeship (through hands-on case studies) and anecdotes (through real-life applications) are the tools that Peter J. Huber uses in this volume. Concern with specific statistical techniques is not of immediate value; rather, questions of strategy ? when to use which technique ? are employed. Central to the discussion is an understanding of the significance of massive (or robust) data sets, the implementation of languages, and the use of models. Each is sprinkled with an ample number of examples and case studies. Personal practices, various pitfalls, and existing controversies are presented when applicable. The book serves as an excellent philosophical and historical companion to any present-day text in data analysis, robust statistics, data mining, statistical learning, or computational statistics.
ISBN: 978-0-470-64338-9
Hardcover
368 pages
March 2011
This book shows readers how to design and set up basic mixture experiments, then analyze the data and draw inferences from the results. It encompasses useful techniques and provides worked examples for every method used. It is an abridged version of the authorfs best-selling, more advanced title on EXPERIMENTS WITH MIXTURES, along with additional exercises, further transitional commentary, new material on generalized linear models and mixture transformations, and new examples where appropriate. Written with the practitioner in mind, computing formulas (rather than mathematical derivations) for key methods are provided with clear and concise explanations. All of the numerical examples are taken from real experiments. Coverage begins with the original mixture problem and ends with an introduction to the analysis of variance. Topics are of interest to the various fields of agriculture such as food science, entomology, and nematology, as well as in the physical sciences (including engineering) and medicine. With brevity as a primary goal, the book is applicable for a one-semester course in design of experiments