Rigid Germs The Valuative Tree And Applications To Kato Varieties

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Rigid Germs, the Valuative Tree, and Applications to Kato Varieties

Author : Matteo Ruggiero
Publisher : Springer
ISBN 13 : 8876425594
Total Pages : 194 pages
Book Rating : 4.8/5 (764 download)

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Book Synopsis Rigid Germs, the Valuative Tree, and Applications to Kato Varieties by : Matteo Ruggiero

Download or read book Rigid Germs, the Valuative Tree, and Applications to Kato Varieties written by Matteo Ruggiero and published by Springer. This book was released on 2016-04-28 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations

Author : Maria Colombo
Publisher : Springer
ISBN 13 : 8876426078
Total Pages : 285 pages
Book Rating : 4.8/5 (764 download)

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Book Synopsis Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations by : Maria Colombo

Download or read book Flows of Non-Smooth Vector Fields and Degenerate Elliptic Equations written by Maria Colombo and published by Springer. This book was released on 2017-06-07 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Tropical Geometry and Mirror Symmetry

Author : Mark Gross
Publisher : American Mathematical Soc.
ISBN 13 : 0821852329
Total Pages : 338 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tropical Geometry and Mirror Symmetry by : Mark Gross

Download or read book Tropical Geometry and Mirror Symmetry written by Mark Gross and published by American Mathematical Soc.. This book was released on 2011-01-20 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Valuative Tree

Author : Charles Favre
Publisher : Springer
ISBN 13 : 354044646X
Total Pages : 251 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis The Valuative Tree by : Charles Favre

Download or read book The Valuative Tree written by Charles Favre and published by Springer. This book was released on 2004-08-30 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Life Interpretation and the Sense of Illness within the Human Condition

Author : Anna-Teresa Tymieniecka
Publisher : Springer Science & Business Media
ISBN 13 : 9401007802
Total Pages : 293 pages
Book Rating : 4.4/5 (1 download)

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Book Synopsis Life Interpretation and the Sense of Illness within the Human Condition by : Anna-Teresa Tymieniecka

Download or read book Life Interpretation and the Sense of Illness within the Human Condition written by Anna-Teresa Tymieniecka and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: In medicine the understanding and interpretation of the complex reality of illness currently refers either to an organismic approach that focuses on the physical or to a 'holistic' approach that takes into account the patient's human sociocultural involvement. Yet as the papers of this collection show, the suffering human person refers ultimately to his/her existential sphere. Hence, praxis is supplemented by still other perspectives for valuation and interpretation: ethical, spiritual, and religious. Can medicine ignore these considerations or push them to the side as being subjective and arbitrary? Phenomenology/philosophy-of-life recognizes all of the above approaches to be essential facets of the Human Condition (Tymieniecka). This approach holds that all the facets of the Human Condition have equal objectivity and legitimacy. It completes the accepted medical outlook and points the way toward a new `medical humanism'.

Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities

Author : William Gignac
Publisher : American Mathematical Society
ISBN 13 : 1470449587
Total Pages : 100 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities by : William Gignac

Download or read book Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities written by William Gignac and published by American Mathematical Society. This book was released on 2021-11-16 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Schottky Groups and Mumford Curves

Author : L. Gerritzen
Publisher : Springer
ISBN 13 : 3540383042
Total Pages : 326 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Schottky Groups and Mumford Curves by : L. Gerritzen

Download or read book Schottky Groups and Mumford Curves written by L. Gerritzen and published by Springer. This book was released on 2006-11-14 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt:

J-holomorphic Curves and Symplectic Topology

Author : Dusa McDuff
Publisher : American Mathematical Soc.
ISBN 13 : 0821887467
Total Pages : 744 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis J-holomorphic Curves and Symplectic Topology by : Dusa McDuff

Download or read book J-holomorphic Curves and Symplectic Topology written by Dusa McDuff and published by American Mathematical Soc.. This book was released on 2012 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

From Groups to Geometry and Back

Author : Vaughn Climenhaga
Publisher : American Mathematical Soc.
ISBN 13 : 1470434792
Total Pages : 442 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis From Groups to Geometry and Back by : Vaughn Climenhaga

Download or read book From Groups to Geometry and Back written by Vaughn Climenhaga and published by American Mathematical Soc.. This book was released on 2017-04-07 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Logic Colloquium '85

Author : The Paris Logic The Paris Logic Group
Publisher : Elsevier
ISBN 13 : 0444535829
Total Pages : 323 pages
Book Rating : 4.4/5 (445 download)

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Book Synopsis Logic Colloquium '85 by : The Paris Logic The Paris Logic Group

Download or read book Logic Colloquium '85 written by The Paris Logic The Paris Logic Group and published by Elsevier. This book was released on 1987-01-01 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analysing Media Texts

Author : Andrew Burn
Publisher : Bloomsbury Publishing
ISBN 13 : 1441169415
Total Pages : 103 pages
Book Rating : 4.4/5 (411 download)

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Book Synopsis Analysing Media Texts by : Andrew Burn

Download or read book Analysing Media Texts written by Andrew Burn and published by Bloomsbury Publishing. This book was released on 2003-12-01 with total page 103 pages. Available in PDF, EPUB and Kindle. Book excerpt: Andrew Burn and David Parker outline how multi-modality theory can be used to analyze texts whicj employ multiple semiotic modes and media, in such a way that a balanced consideration is given to the characteristics of each mode, how they integrate, and how they distribute textual functions between them. The medthods are rooted in a view of significance as dependent on social context, and fulfilling the social and communicative interests of both producers of textual production and use contingent upon digital formats will also be a determining content of the analytical method.

Opera de Cribro

Author : John B. Friedlander
Publisher : American Mathematical Soc.
ISBN 13 : 0821849700
Total Pages : 554 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Opera de Cribro by : John B. Friedlander

Download or read book Opera de Cribro written by John B. Friedlander and published by American Mathematical Soc.. This book was released on 2010-06-22 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mirror Symmetry and Tropical Geometry

Author : Ricardo Castaño-Bernard
Publisher : American Mathematical Soc.
ISBN 13 : 0821858513
Total Pages : 184 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Mirror Symmetry and Tropical Geometry by : Ricardo Castaño-Bernard

Download or read book Mirror Symmetry and Tropical Geometry written by Ricardo Castaño-Bernard and published by American Mathematical Soc.. This book was released on 2010 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Pushing Limits

Author : Ted Hill
Publisher : American Mathematical Soc.
ISBN 13 : 1470435845
Total Pages : 331 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Pushing Limits by : Ted Hill

Download or read book Pushing Limits written by Ted Hill and published by American Mathematical Soc.. This book was released on 2017-04-03 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Matheon--mathematics for Key Technologies

Author : Peter Deuflhard
Publisher : Susaeta
ISBN 13 : 9783037191378
Total Pages : 472 pages
Book Rating : 4.1/5 (913 download)

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Book Synopsis Matheon--mathematics for Key Technologies by : Peter Deuflhard

Download or read book Matheon--mathematics for Key Technologies written by Peter Deuflhard and published by Susaeta. This book was released on 2014 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics: intellectual endeavor, production factor, key technology, key to key technologies? Mathematics is all of these; the last three of its facets are not well known, though. They have been the focus of the research and development in the Berlin-based DFG Research Center MATHEON in the last twelve years. Through these activities, MATHEON has become an international trademark. Its mission and its strategies for carrying out creative, application-driven research in mathematics and cooperating in the solution of complex problems in key technologies are by now a role model for the development of many other centers. Modern key technologies have become highly sophisticated, integrating aspects of engineering, computer, business and other sciences. At the same time, the innovation cycles get shorter and shorter. These simultaneous challenges can be mastered only by qualitatively and quantitatively rigorous methods. And that is where mathematics is indispensable. Flexible mathematical models, as well as fast and accurate methods for numerical simulation and optimization, open new possibilities to handle the indicated complexities, to react quickly, and to explore new options. Researchers in mathematical fields such as optimization, discrete mathematics, numerical analysis, scientific computing, applied analysis and stochastic analysis have to work hand in hand with scientists and engineers to fully exploit this potential and to strengthen the transversal role of mathematics in solving the challenging problems in key technologies. This book presents in seven chapters the research highlights of the research work carried out in the MATHEON application areas: Life Sciences, Networks, Production, Electronic and Photonic Devices, Finance, Visualization, and Education. The chapters summarize many of the contributions, put them in the context of current mathematical research activities, and outline their impact in various key technologies. To make some of the results more easily accessible to the general public, a large number of ``showcases'' are presented that illustrate a few success stories.

Arithmetic and Geometry over Local Fields

Author : Bruno Anglès
Publisher : Springer Nature
ISBN 13 : 3030662497
Total Pages : 337 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Arithmetic and Geometry over Local Fields by : Bruno Anglès

Download or read book Arithmetic and Geometry over Local Fields written by Bruno Anglès and published by Springer Nature. This book was released on 2021-03-03 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces some recent developments in Arithmetic Geometry over local fields. Its seven chapters are centered around two common themes: the study of Drinfeld modules and non-Archimedean analytic geometry. The notes grew out of lectures held during the research program "Arithmetic and geometry of local and global fields" which took place at the Vietnam Institute of Advanced Study in Mathematics (VIASM) from June to August 2018. The authors, leading experts in the field, have put great effort into making the text as self-contained as possible, introducing the basic tools of the subject. The numerous concrete examples and suggested research problems will enable graduate students and young researchers to quickly reach the frontiers of this fascinating branch of mathematics.

Geometric Stability Theory

Author : Anand Pillay
Publisher : Oxford University Press on Demand
ISBN 13 : 9780198534372
Total Pages : 361 pages
Book Rating : 4.5/5 (343 download)

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Book Synopsis Geometric Stability Theory by : Anand Pillay

Download or read book Geometric Stability Theory written by Anand Pillay and published by Oxford University Press on Demand. This book was released on 1996 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.