Rigid Germs The Valuative Tree And Applications To Kato Varieties

Author : Matteo Ruggiero
Publisher : Springer
Page : 194 pages
File Size : 48,8 Mb
Release : 2016-04-28
Category : Mathematics
ISBN : 9788876425592

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Rigid Germs, the Valuative Tree, and Applications to Kato Varieties by Matteo Ruggiero Pdf

This thesis deals with specific features of the theory of holomorphic dynamics in dimension 2 and then sets out to study analogous questions in higher dimensions, e.g. dealing with normal forms for rigid germs, and examples of Kato 3-folds. The local dynamics of holomorphic maps around critical points is still not completely understood, in dimension 2 or higher, due to the richness of the geometry of the critical set for all iterates. In dimension 2, the study of the dynamics induced on a suitable functional space (the valuative tree) allows a classification of such maps up to birational conjugacy, reducing the problem to the special class of rigid germs, where the geometry of the critical set is simple. In some cases, from such dynamical data one can construct special compact complex surfaces, called Kato surfaces, related to some conjectures in complex geometry.

Author : Maria Colombo
Publisher : Springer
Page : 250 pages
File Size : 52,5 Mb
Release : 2017-06-07
Category : Mathematics
ISBN : 9788876426070

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Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations by Maria Colombo Pdf

The first part of the book is devoted to the transport equation for a given vector field, exploiting the lagrangian structure of solutions. It also treats the regularity of solutions of some degenerate elliptic equations, which appear in the eulerian counterpart of some transport models with congestion. The second part of the book deals with the lagrangian structure of solutions of the Vlasov-Poisson system, which describes the evolution of a system of particles under the self-induced gravitational/electrostatic field, and the existence of solutions of the semigeostrophic system, used in meteorology to describe the motion of large-scale oceanic/atmospheric flows.​

Author : Mark Gross
Publisher : American Mathematical Soc.
Page : 338 pages
File Size : 50,8 Mb
Release : 2011-01-20
Category : Mathematics
ISBN : 9780821852323

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Tropical Geometry and Mirror Symmetry by Mark Gross Pdf

Tropical geometry provides an explanation for the remarkable power of mirror symmetry to connect complex and symplectic geometry. The main theme of this book is the interplay between tropical geometry and mirror symmetry, culminating in a description of the recent work of Gross and Siebert using log geometry to understand how the tropical world relates the A- and B-models in mirror symmetry. The text starts with a detailed introduction to the notions of tropical curves and manifolds, and then gives a thorough description of both sides of mirror symmetry for projective space, bringing together material which so far can only be found scattered throughout the literature. Next follows an introduction to the log geometry of Fontaine-Illusie and Kato, as needed for Nishinou and Siebert's proof of Mikhalkin's tropical curve counting formulas. This latter proof is given in the fourth chapter. The fifth chapter considers the mirror, B-model side, giving recent results of the author showing how tropical geometry can be used to evaluate the oscillatory integrals appearing. The final chapter surveys reconstruction results of the author and Siebert for ``integral tropical manifolds.'' A complete version of the argument is given in two dimensions.

Author : Charles Favre,Mattias Jonsson
Publisher : Springer
Page : 244 pages
File Size : 52,8 Mb
Release : 2004-08-30
Category : Mathematics
ISBN : 9783540446460

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The Valuative Tree by Charles Favre,Mattias Jonsson Pdf

This volume is devoted to a beautiful object, called the valuative tree and designed as a powerful tool for the study of singularities in two complex dimensions. Its intricate yet manageable structure can be analyzed by both algebraic and geometric means. Many types of singularities, including those of curves, ideals, and plurisubharmonic functions, can be encoded in terms of positive measures on the valuative tree. The construction of these measures uses a natural tree Laplace operator of independent interest.

Author : L. Gerritzen,M. van der Put
Publisher : Springer
Page : 326 pages
File Size : 47,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540383048

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Schottky Groups and Mumford Curves by L. Gerritzen,M. van der Put Pdf

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 43,8 Mb
Release : 1985
Category : Electronic
ISBN : OCLC:1037107278

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Magic, Witchcraft, and Religion by Anonim Pdf

Author : William Gignac,Matteo Ruggiero
Publisher : American Mathematical Society
Page : 100 pages
File Size : 45,9 Mb
Release : 2021-11-16
Category : Mathematics
ISBN : 9781470449582

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Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities by William Gignac,Matteo Ruggiero Pdf

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Author : Dusa McDuff,Dietmar Salamon
Publisher : American Mathematical Soc.
Page : 744 pages
File Size : 53,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821887462

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J-holomorphic Curves and Symplectic Topology by Dusa McDuff,Dietmar Salamon Pdf

The main goal of this book is to establish the fundamental theorems of the subject in full and rigourous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associatively of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology.

Author : The Paris Logic Group
Publisher : Elsevier
Page : 308 pages
File Size : 45,5 Mb
Release : 1987-01-01
Category : Mathematics
ISBN : 9780444535825

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Logic Colloquium '85 by The Paris Logic Group Pdf

The bulk of this volume consists of invited addresses presented at the Colloquium. These contributions report on recent or ongoing research in some of the mainstream areas of mathematical logic: model theory, both pure and in its applications (to group theory and real algebraic geometry); and proof theory, applied to set theory and diophantine equations. The major novel aspect of the book is the important place accorded to the connections of mathematical logic with the neighboring disciplines: mathematical foundations of computer science, and philosophy of mathematics.

Author : Terrence Walters,Roy Osborne
Publisher : CABI
Page : 267 pages
File Size : 44,6 Mb
Release : 2004-01
Category : Literary Criticism
ISBN : 0851997414

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Cycad Classification by Terrence Walters,Roy Osborne Pdf

This volume presents the current state of our knowledge of the classification of the approximately 300 species of cycads. It includes contributions from leading researchers from Australia, China, Italy, Mexico, South Africa, Thailand and the USA. It has been developed from papers presented at a workshop held in 2002 at the Montgomery Botanical Center. The book provides guidelines for the designation of species, species boundaries and species groupings, thus clarifying what has been a confused area of research.

Author : Vaughn Climenhaga,Anatole Katok
Publisher : American Mathematical Soc.
Page : 420 pages
File Size : 54,7 Mb
Release : 2017-04-07
Category : Geometry
ISBN : 9781470434793

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From Groups to Geometry and Back by Vaughn Climenhaga,Anatole Katok Pdf

Groups arise naturally as symmetries of geometric objects, and so groups can be used to understand geometry and topology. Conversely, one can study abstract groups by using geometric techniques and ultimately by treating groups themselves as geometric objects. This book explores these connections between group theory and geometry, introducing some of the main ideas of transformation groups, algebraic topology, and geometric group theory. The first half of the book introduces basic notions of group theory and studies symmetry groups in various geometries, including Euclidean, projective, and hyperbolic. The classification of Euclidean isometries leads to results on regular polyhedra and polytopes; the study of symmetry groups using matrices leads to Lie groups and Lie algebras. The second half of the book explores ideas from algebraic topology and geometric group theory. The fundamental group appears as yet another group associated to a geometric object and turns out to be a symmetry group using covering spaces and deck transformations. In the other direction, Cayley graphs, planar models, and fundamental domains appear as geometric objects associated to groups. The final chapter discusses groups themselves as geometric objects, including a gentle introduction to Gromov's theorem on polynomial growth and Grigorchuk's example of intermediate growth. The book is accessible to undergraduate students (and anyone else) with a background in calculus, linear algebra, and basic real analysis, including topological notions of convergence and connectedness. This book is a result of the MASS course in algebra at Penn State University in the fall semester of 2009.

Author : John B. Friedlander,Henryk Iwaniec
Publisher : American Mathematical Soc.
Page : 554 pages
File Size : 46,6 Mb
Release : 2010-06-22
Category : Mathematics
ISBN : 9780821849705

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Opera de Cribro by John B. Friedlander,Henryk Iwaniec Pdf

This is a true masterpiece that will prove to be indispensable to the serious researcher for many years to come. --Enrico Bombieri, Institute for Advanced Study This is a truly comprehensive account of sieves and their applications, by two of the world's greatest authorities. Beginners will find a thorough introduction to the subject, with plenty of helpful motivation. The more practised reader will appreciate the authors' insights into some of the more mysterious parts of the theory, as well as the wealth of new examples. --Roger Heath-Brown, University of Oxford, Fellow of Royal Society This is a comprehensive and up-to-date treatment of sieve methods. The theory of the sieve is developed thoroughly with complete and accessible proofs of the basic theorems. Included is a wide range of applications, both to traditional questions such as those concerning primes, and to areas previously unexplored by sieve methods, such as elliptic curves, points on cubic surfaces and quantum ergodicity. New proofs are given also of some of the central theorems of analytic number theory; these proofs emphasize and take advantage of the applicability of sieve ideas. The book contains numerous comments which provide the reader with insight into the workings of the subject, both as to what the sieve can do and what it cannot do. The authors reveal recent developements by which the parity barrier can be breached, exposing golden nuggets of the subject, previously inaccessible. The variety in the topics covered and in the levels of difficulty encountered makes this a work of value to novices and experts alike, both as an educational tool and a basic reference.

Author : Ricardo Castaño-Bernard,Yan S. Soibelman,Ilia Zharkov
Publisher : American Mathematical Soc.
Page : 184 pages
File Size : 43,5 Mb
Release : 2010
Category : Science
ISBN : 9780821858516

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Mirror Symmetry and Tropical Geometry by Ricardo Castaño-Bernard,Yan S. Soibelman,Ilia Zharkov Pdf

This volume contains contributions from the NSF-CBMS Conference on Tropical Geometry and Mirror Symmetry, which was held from December 13-17, 2008 at Kansas State University in Manhattan, Kansas. It gives an excellent picture of numerous connections of mirror symmetry with other areas of mathematics (especially with algebraic and symplectic geometry) as well as with other areas of mathematical physics. The techniques and methods used by the authors of the volume are at the frontier of this very active area of research.

Author : Ted Hill
Publisher : American Mathematical Soc.
Page : 294 pages
File Size : 49,9 Mb
Release : 2017-04-03
Category : Hill, Theodore Preston
ISBN : 9781470435844

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Pushing Limits by Ted Hill Pdf

Pushing Limits: From West Point to Berkeley and Beyond challenges the myth that mathematicians lead dull and ascetic lives. It recounts the unique odyssey of a noted mathematician who overcame military hurdles at West Point, Army Ranger School and the Vietnam War, and survived many civilian escapades—hitchhiking in third-world hotspots, fending off sharks in Bahamian reefs, and camping deep behind the forbidding Iron Curtain. From ultra-conservative West Point in the ’60s to ultra-radical Berkeley in the ’70s, and ultimately to genteel Georgia Tech in the ’80s, this is the tale of an academic career as noteworthy for its offbeat adventures as for its teaching and research accomplishments. It brings to life the struggles and risks underlying mathematical research, the unparalleled thrill of making scientific breakthroughs, and the joy of sharing those discoveries around the world. Hill's book is packed with energy, humor, and suspense, both physical and intellectual. Anyone who is curious about how one maverick mathematician thinks, who wants to relive the zanier side of the ’60s and ’70s, who wants an armchair journey into the third world, or who seeks an unconventional view of several of society's iconic institutions, will be drawn to this book.

Author : Anand Pillay,Professor of Mathematics Anand Pillay
Publisher : Oxford University Press on Demand
Page : 361 pages
File Size : 43,9 Mb
Release : 1996
Category : Language Arts & Disciplines
ISBN : 019853437X

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Geometric Stability Theory by Anand Pillay,Professor of Mathematics Anand Pillay Pdf

This book is an exposition of the central features of one of the most developed and sophisticated parts of modern model theory. Geometric stability theory studies the fine structure of models of stable theories. An ever present theme is the existence and structure of definable groups.Fundamental applications to a classification theory are included in the text. Recent years have seen other surprising applications to, among other things, diophantine geometry. This book will be invaluable to anyone interested in modern model theory, such as working model theorists and graduatestudents in logic.