Download or read book Moduli Spaces and Locally Symmetric Spaces written by Lizhen Ji and published by . This book was released on 2021-10-30 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides accessible and systematic introductions to moduli spaces of Riemann surfaces, algebraic curves, moduli spaces of vector bundles on Riemann surfaces, moduli spaces of singularities, and compactification of a natural class of locally symmetric spaces.

Download or read book Compactifications of Symmetric Spaces written by Yves Guivarc'h and published by Springer Science & Business Media. This book was released on 1998-08-26 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of symmetric space is of central importance in many branches of mathematics. Compactifications of these spaces have been studied from the points of view of representation theory, geometry, and random walks. This work is devoted to the study of the interrelationships among these various compactifications and, in particular, focuses on the martin compactifications. It is the first exposition to treat compactifications of symmetric spaces systematically and to uniformized the various points of view. The work is largely self-contained, with comprehensive references to the literature. It is an excellent resource for both researchers and graduate students.

Download or read book Strong Rigidity of Locally Symmetric Spaces written by G. Daniel Mostow and published by Princeton University Press. This book was released on 1973-12-21 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Locally symmetric spaces are generalizations of spaces of constant curvature. In this book the author presents the proof of a remarkable phenomenon, which he calls "strong rigidity": this is a stronger form of the deformation rigidity that has been investigated by Selberg, Calabi-Vesentini, Weil, Borel, and Raghunathan. The proof combines the theory of semi-simple Lie groups, discrete subgroups, the geometry of E. Cartan's symmetric Riemannian spaces, elements of ergodic theory, and the fundamental theorem of projective geometry as applied to Tit's geometries. In his proof the author introduces two new notions having independent interest: one is "pseudo-isometries"; the other is a notion of a quasi-conformal mapping over the division algebra K (K equals real, complex, quaternion, or Cayley numbers). The author attempts to make the account accessible to readers with diverse backgrounds, and the book contains capsule descriptions of the various theories that enter the proof.

Download or read book Compactifications of Symmetric and Locally Symmetric Spaces written by Armand Borel and published by Springer Science & Business Media. This book was released on 2006-07-25 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces uniform constructions of most of the known compactifications of symmetric and locally symmetric spaces, with emphasis on their geometric and topological structures Relatively self-contained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to analysis, number theory, algebraic geometry and algebraic topology

Download or read book Locally Mixed Symmetric Spaces written by Bruce Hunt and published by Springer Nature. This book was released on 2021-09-04 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common? All are related to a type of manifold called locally mixed symmetric spaces in this book. The presentation emphasizes geometric concepts and relations and gives each reader the "roter Faden", starting from the basics and proceeding towards quite advanced topics which lie at the intersection of differential and algebraic geometry, algebra and topology. Avoiding technicalities and assuming only a working knowledge of real Lie groups, the text provides a wealth of examples of symmetric spaces. The last two chapters deal with one particular case (Kuga fiber spaces) and a generalization (elliptic surfaces), both of which require some knowledge of algebraic geometry. Of interest to topologists, differential or algebraic geometers working in areas related to arithmetic groups, the book also offers an introduction to the ideas for non-experts.

Download or read book Moduli of Curves and Abelian Varieties written by Carel Faber and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Dutch Intercity Seminar on Moduli, which dates back to the early eighties, was an initiative of G. van der Geer, F. Oort and C. Peters. Through the years it became a focal point of Dutch mathematics and it gained some fame, also outside Holland, as an active biweekly research seminar. The tradition continues up to today. The present volume, with contributions of R. Dijkgraaf, C. Faber, G. van der Geer, R. Hain, E. Looijenga, and F. Oort, originates from the seminar held in 1995--96. Some of the articles here were discussed, in preliminary form, in the seminar; others are completely new. Two introductory papers, on moduli of abelian varieties and on moduli of curves, accompany the articles.

Download or read book Locally Symmetric Spaces written by Isidore Bernard Fleischer and published by . This book was released on 1952 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Generalized Symmetric Spaces written by O. Kowalski and published by Lecture Notes in Mathematics. This book was released on 1980-06 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Symmetric Spaces Short Courses Presented at Washington University written by William Munger Boothby and published by . This book was released on 1972 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Foundations of Symmetric Spaces of Measurable Functions written by Ben-Zion A. Rubshtein and published by Springer. This book was released on 2016-12-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Key definitions and results in symmetric spaces, particularly Lp, Lorentz, Marcinkiewicz and Orlicz spaces are emphasized in this textbook. A comprehensive overview of the Lorentz, Marcinkiewicz and Orlicz spaces is presented based on concepts and results of symmetric spaces. Scientists and researchers will find the application of linear operators, ergodic theory, harmonic analysis and mathematical physics noteworthy and useful. This book is intended for graduate students and researchers in mathematics and may be used as a general reference for the theory of functions, measure theory, and functional analysis. This self-contained text is presented in four parts totaling seventeen chapters to correspond with a one-semester lecture course. Each of the four parts begins with an overview and is subsequently divided into chapters, each of which concludes with exercises and notes. A chapter called “Complements” is included at the end of the text as supplementary material to assist students with independent work.

Download or read book The Geometry of Moduli Spaces of Sheaves written by Daniel Huybrechts and published by Cambridge University Press. This book was released on 2010-05-27 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition has been updated to reflect recent advances in the theory of semistable coherent sheaves and their moduli spaces. The authors review changes in the field and point the reader towards further literature. An ideal text for graduate students or mathematicians with a background in algebraic geometry.

Download or read book Moduli Spaces of Riemann Surfaces written by Benson Farb and published by American Mathematical Soc.. This book was released on 2013-08-16 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Download or read book Geometry of Moduli Spaces and Representation Theory written by Roman Bezrukavnikov and published by American Mathematical Soc.. This book was released on 2017-12-15 with total page 449 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on lectures given at the Graduate Summer School of the 2015 Park City Mathematics Institute program “Geometry of moduli spaces and representation theory”, and is devoted to several interrelated topics in algebraic geometry, topology of algebraic varieties, and representation theory. Geometric representation theory is a young but fast developing research area at the intersection of these subjects. An early profound achievement was the famous conjecture by Kazhdan–Lusztig about characters of highest weight modules over a complex semi-simple Lie algebra, and its subsequent proof by Beilinson-Bernstein and Brylinski-Kashiwara. Two remarkable features of this proof have inspired much of subsequent development: intricate algebraic data turned out to be encoded in topological invariants of singular geometric spaces, while proving this fact required deep general theorems from algebraic geometry. Another focus of the program was enumerative algebraic geometry. Recent progress showed the role of Lie theoretic structures in problems such as calculation of quantum cohomology, K-theory, etc. Although the motivation and technical background of these constructions is quite different from that of geometric Langlands duality, both theories deal with topological invariants of moduli spaces of maps from a target of complex dimension one. Thus they are at least heuristically related, while several recent works indicate possible strong technical connections. The main goal of this collection of notes is to provide young researchers and experts alike with an introduction to these areas of active research and promote interaction between the two related directions.

Download or read book The Local Geometry of the Moduli Space of Calabi Yau Manifolds written by Dipankar Ray and published by . This book was released on 1999 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Generalized Triangle Inequalities in Symmetric Spaces and Buildings with Applications to Algebra written by Michael Kapovich and published by American Mathematical Soc.. This book was released on 2008 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors apply their results on the geometry of polygons in infinitesimal symmetric spaces and symmetric spaces and buildings to four problems in algebraic group theory. Two of these problems are generalizations of the problems of finding the constraints on the eigenvalues (resp. singular values) of a sum (resp. product) when the eigenvalues (singular values) of each summand (factor) are fixed. The other two problems are related to the nonvanishing of the structure constants of the (spherical) Hecke and representation rings associated with a split reductive algebraic group over $\mathbb{Q}$ and its complex Langlands' dual. The authors give a new proof of the Saturation Conjecture for $GL(\ell)$ as a consequence of their solution of the corresponding saturation problem for the Hecke structure constants for all split reductive algebraic groups over $\mathbb{Q}$.

Download or read book On Locally Symmetric Spaces of Arithmetic Type written by Youichi Saigusa and published by . This book was released on 1971 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lecture Notes in Mathematics written by and published by . This book was released on 1964 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: