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Tropical Algebraic Geometry

Tropical Algebraic Geometry Author Ilia Itenberg
ISBN-10 3034600488
Release 2009-05-30
Pages 104
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These notes present a polished introduction to tropical geometry and contain some applications of this rapidly developing and attractive subject. It consists of three chapters which complete each other and give a possibility for non-specialists to make the first steps in the subject which is not yet well represented in the literature. The notes are based on a seminar at the Mathematical Research Center in Oberwolfach in October 2004. The intended audience is graduate, post-graduate, and Ph.D. students as well as established researchers in mathematics.

Algebraic and Combinatorial Aspects of Tropical Geometry

Algebraic and Combinatorial Aspects of Tropical Geometry Author Erwan Brugalle
ISBN-10 9780821891469
Release 2013-05-23
Pages 350
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This volume contains the proceedings of the CIEM workshop on Tropical Geometry, held December 12-16, 2011, at the International Centre for Mathematical Meetings (CIEM), Castro Urdiales, Spain. Tropical geometry is a new and rapidly developing field of mat

Tropical Geometry and Integrable Systems

Tropical Geometry and Integrable Systems Author Chris Athorne
ISBN-10 9780821875537
Release 2012
Pages 155
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This volume contains the proceedings of the conference on tropical geometry and integrable systems, held July 3-8, 2011, at the University of Glasgow, United Kingdom. One of the aims of this conference was to bring together researchers in the field of tropical geometry and its applications, from apparently disparate ends of the spectrum, to foster a mutual understanding and establish a common language which will encourage further developments of the area. This aim is reflected in these articles, which cover areas from automata, through cluster algebras, to enumerative geometry. In addition, two survey articles are included which introduce ideas from researchers on one end of this spectrum to researchers on the other. This book is intended for graduate students and researchers interested in tropical geometry and integrable systems and the developing links between these two areas.

Analysis Meets Geometry

Analysis Meets Geometry Author Mats Andersson
ISBN-10 9783319524719
Release 2017-09-04
Pages 466
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This book is dedicated to the memory of Mikael Passare, an outstanding Swedish mathematician who devoted his life to developing the theory of analytic functions in several complex variables and exploring geometric ideas first-hand. It includes several papers describing Mikael’s life as well as his contributions to mathematics, written by friends of Mikael’s who share his attitude and passion for science. A major section of the book presents original research articles that further develop Mikael’s ideas and which were written by his former students and co-authors. All these mathematicians work at the interface of analysis and geometry, and Mikael’s impact on their research cannot be underestimated. Most of the contributors were invited speakers at the conference organized at Stockholm University in his honor. This book is an attempt to express our gratitude towards this great mathematician, who left us full of energy and new creative mathematical ideas.

Introduction to Tropical Geometry

Introduction to Tropical Geometry Author Diane Maclagan
ISBN-10 9780821851982
Release 2015-04-15
Pages 363
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Tropical geometry is a combinatorial shadow of algebraic geometry, offering new polyhedral tools to compute invariants of algebraic varieties. It is based on tropical algebra, where the sum of two numbers is their minimum and the product is their sum. This turns polynomials into piecewise-linear functions, and their zero sets into polyhedral complexes. These tropical varieties retain a surprising amount of information about their classical counterparts. Tropical geometry is a young subject that has undergone a rapid development since the beginning of the 21st century. While establishing itself as an area in its own right, deep connections have been made to many branches of pure and applied mathematics. This book offers a self-contained introduction to tropical geometry, suitable as a course text for beginning graduate students. Proofs are provided for the main results, such as the Fundamental Theorem and the Structure Theorem. Numerous examples and explicit computations illustrate the main concepts. Each of the six chapters concludes with problems that will help the readers to practice their tropical skills, and to gain access to the research literature.

Algebraic Statistics for Computational Biology

Algebraic Statistics for Computational Biology Author L. Pachter
ISBN-10 0521857007
Release 2005-08-22
Pages 420
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This book, first published in 2005, offers an introduction to the application of algebraic statistics to computational biology.

Annales Scientifiques de L cole Normale Sup rieure

Annales Scientifiques de L   cole Normale Sup  rieure Author École normale supérieure (France)
ISBN-10 MINN:31951P01108300C
Release 2010
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Annales Scientifiques de L cole Normale Sup rieure has been writing in one form or another for most of life. You can find so many inspiration from Annales Scientifiques de L cole Normale Sup rieure also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Annales Scientifiques de L cole Normale Sup rieure book for free.

Moduli Spaces of Riemannian Metrics

Moduli Spaces of Riemannian Metrics Author Wilderich Tuschmann
ISBN-10 9783034809481
Release 2015-10-14
Pages 123
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This book studies certain spaces of Riemannian metrics on both compact and non-compact manifolds. These spaces are defined by various sign-based curvature conditions, with special attention paid to positive scalar curvature and non-negative sectional curvature, though we also consider positive Ricci and non-positive sectional curvature. If we form the quotient of such a space of metrics under the action of the diffeomorphism group (or possibly a subgroup) we obtain a moduli space. Understanding the topology of both the original space of metrics and the corresponding moduli space form the central theme of this book. For example, what can be said about the connectedness or the various homotopy groups of such spaces? We explore the major results in the area, but provide sufficient background so that a non-expert with a grounding in Riemannian geometry can access this growing area of research.

Basic Algebraic Geometry 1

Basic Algebraic Geometry 1 Author Igor R. Shafarevich
ISBN-10 9783642379567
Release 2013-08-13
Pages 310
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Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.'' The third edition, in addition to some minor corrections, now offers a new treatment of the Riemann--Roch theorem for curves, including a proof from first principles. Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field.

Cluster Algebras and Poisson Geometry

Cluster Algebras and Poisson Geometry Author Michael Gekhtman
ISBN-10 9780821849729
Release 2010
Pages 246
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Cluster algebras, introduced by Fomin and Zelevinsky in 2001, are commutative rings with unit and no zero divisors equipped with a distinguished family of generators (cluster variables) grouped in overlapping subsets (clusters) of the same cardinality (the rank of the cluster algebra) connected by exchange relations. Examples of cluster algebras include coordinate rings of many algebraic varieties that play a prominent role in representation theory, invariant theory, the study of total positivity, etc. The theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links to a wide range of subjects including representation theory, discrete dynamical systems, Teichmuller theory, and commutative and non-commutative algebraic geometry. This book is the first devoted to cluster algebras. After presenting the necessary introductory material about Poisson geometry and Schubert varieties in the first two chapters, the authors introduce cluster algebras and prove their main properties in Chapter 3. This chapter can be viewed as a primer on the theory of cluster algebras. In the remaining chapters, the emphasis is made on geometric aspects of the cluster algebra theory, in particular on its relations to Poisson geometry and to the theory of integrable systems.

Topological Methods in Algebraic Geometry

Topological Methods in Algebraic Geometry Author Friedrich Hirzebruch
ISBN-10 9783662306970
Release 2013-11-11
Pages 232
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Topological Methods in Algebraic Geometry has been writing in one form or another for most of life. You can find so many inspiration from Topological Methods in Algebraic Geometry also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Topological Methods in Algebraic Geometry book for free.

An Invitation to Algebraic Geometry

An Invitation to Algebraic Geometry Author Karen E. Smith
ISBN-10 9781475744972
Release 2013-03-09
Pages 164
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This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.

Discriminants Resultants and Multidimensional Determinants

Discriminants  Resultants  and Multidimensional Determinants Author Israel M. Gelfand
ISBN-10 9780817647711
Release 2009-05-21
Pages 523
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"This book revives and vastly expands the classical theory of resultants and discriminants. Most of the main new results of the book have been published earlier in more than a dozen joint papers of the authors. The book nicely complements these original papers with many examples illustrating both old and new results of the theory."—Mathematical Reviews

Manis Valuations and Pr fer Extensions I

Manis Valuations and Pr  fer Extensions I Author Manfred Knebusch
ISBN-10 9783540456254
Release 2004-10-20
Pages 274
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The present book is devoted to a study of relative Prüfer rings and Manis valuations, with an eye to application in real and p-adic geometry. If one wants to expand on the usual algebraic geometry over a non-algebraically closed base field, e.g. a real closed field or p-adically closed field, one typically meets lots of valuation domains. Usually they are not discrete and hence not noetherian. Thus, for a further develomemt of real algebraic and real analytic geometry in particular, and certainly also rigid analytic and p-adic geometry, new chapters of commutative algebra are needed, often of a non-noetherian nature. The present volume presents one such chapter.

Homological Mirror Symmetry and Tropical Geometry

Homological Mirror Symmetry and Tropical Geometry Author Ricardo Castano-Bernard
ISBN-10 9783319065144
Release 2014-10-07
Pages 436
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The relationship between Tropical Geometry and Mirror Symmetry goes back to the work of Kontsevich and Y. Soibelman (2000), who applied methods of non-archimedean geometry (in particular, tropical curves) to Homological Mirror Symmetry. In combination with the subsequent work of Mikhalkin on the “tropical” approach to Gromov-Witten theory and the work of Gross and Siebert, Tropical Geometry has now become a powerful tool. Homological Mirror Symmetry is the area of mathematics concentrated around several categorical equivalences connecting symplectic and holomorphic (or algebraic) geometry. The central ideas first appeared in the work of Maxim Kontsevich (1993). Roughly speaking, the subject can be approached in two ways: either one uses Lagrangian torus fibrations of Calabi-Yau manifolds (the so-called Strominger-Yau-Zaslow picture, further developed by Kontsevich and Soibelman) or one uses Lefschetz fibrations of symplectic manifolds (suggested by Kontsevich and further developed by Seidel). Tropical Geometry studies piecewise-linear objects which appear as “degenerations” of the corresponding algebro-geometric objects.

Transcending Tradition Jewish Mathematicians in German Speaking Academic Culture

Transcending Tradition  Jewish Mathematicians in German Speaking Academic Culture Author Birgit Bergmann
ISBN-10 9783642224645
Release 2012-10-22
Pages 289
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A companion publication to the international exhibition "Transcending Tradition: Jewish Mathematicians in German-Speaking Academic Culture", the catalogue explores the working lives and activities of Jewish mathematicians in German-speaking countries during the period between the legal and political emancipation of the Jews in the 19th century and their persecution in Nazi Germany. It highlights the important role Jewish mathematicians played in all areas of mathematical culture during the Wilhelmine Empire and the Weimar Republic, and recalls their emigration, flight or death after 1933.

Nonarchimedean and Tropical Geometry

Nonarchimedean and Tropical Geometry Author Matthew Baker
ISBN-10 9783319309453
Release 2016-08-18
Pages 526
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This volume grew out of two Simons Symposia on "Nonarchimedean and tropical geometry" which took place on the island of St. John in April 2013 and in Puerto Rico in February 2015. Each meeting gathered a small group of experts working near the interface between tropical geometry and nonarchimedean analytic spaces for a series of inspiring and provocative lectures on cutting edge research, interspersed with lively discussions and collaborative work in small groups. The articles collected here, which include high-level surveys as well as original research, mirror the main themes of the two Symposia. Topics covered in this volume include: Differential forms and currents, and solutions of Monge-Ampere type differential equations on Berkovich spaces and their skeletons; The homotopy types of nonarchimedean analytifications; The existence of "faithful tropicalizations" which encode the topology and geometry of analytifications; Relations between nonarchimedean analytic spaces and algebraic geometry, including logarithmic schemes, birational geometry, and the geometry of algebraic curves; Extended notions of tropical varieties which relate to Huber's theory of adic spaces analogously to the way that usual tropical varieties relate to Berkovich spaces; and Relations between nonarchimedean geometry and combinatorics, including deep and fascinating connections between matroid theory, tropical geometry, and Hodge theory.