Ji, Lizhen 1964
Overview
Works:  89 works in 275 publications in 2 languages and 2,702 library holdings 

Genres:  Conference papers and proceedings History Bibliography Handbooks and manuals 
Roles:  Editor, Author, Dedicatee 
Publication Timeline
.
Most widely held works by
Lizhen Ji
Compactifications of symmetric spaces by
Y Guivarc'h(
Book
)
13 editions published between 1996 and 1998 in English and held by 280 WorldCat member libraries worldwide
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. Key features: * definition and detailed analysis of the Martin compactifications * new geometric Compactification, defined in terms of the Tits building, that coincides with the Martin Compactification at the bottom of the positive spectrum. * geometric, noninductive, description of the Karpelevic Compactification * study of the wellknow isomorphism between the Satake compactifications and the Furstenberg compactifications * systematic and clear progression of topics from geometry to analysis, and finally to random walks The work is largely selfcontained, with comprehensive references to the literature. It is an excellent resource for both researchers and graduate students
13 editions published between 1996 and 1998 in English and held by 280 WorldCat member libraries worldwide
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. Key features: * definition and detailed analysis of the Martin compactifications * new geometric Compactification, defined in terms of the Tits building, that coincides with the Martin Compactification at the bottom of the positive spectrum. * geometric, noninductive, description of the Karpelevic Compactification * study of the wellknow isomorphism between the Satake compactifications and the Furstenberg compactifications * systematic and clear progression of topics from geometry to analysis, and finally to random walks The work is largely selfcontained, with comprehensive references to the literature. It is an excellent resource for both researchers and graduate students
Compactifications of symmetric and locally symmetric spaces by
Armand Borel(
Book
)
22 editions published between 2006 and 2008 in English and held by 240 WorldCat member libraries worldwide
Noncompact symmetric and locally symmetric spaces naturally appear in many mathematical theories, including analysis (representation theory, nonabelian harmonic analysis), number theory (automorphic forms), algebraic geometry (modulae) and algebraic topology (cohomology of discrete groups). In most applications it is necessary to form an appropriate compactification of the space. The literature dealing with such compactifications is vast. The main purpose of this book is to introduce uniform constructions of most of the known compactifications with emphasis on their geometric and topological structures. The book is divided into three parts. Part I studies compactifications of Riemannian symmetric spaces and their arithmetic quotients. Part II is a study of compact smooth manifolds. Part III studies the compactification of locally symmetric spaces. Familiarity with the theory of semisimple Lie groups is assumed, as is familiarity with algebraic groups defined over the rational numbers in later parts of the book, although most of the pertinent material is recalled as presented. Otherwise, the book is a selfcontained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to diverse fields of mathematics
22 editions published between 2006 and 2008 in English and held by 240 WorldCat member libraries worldwide
Noncompact symmetric and locally symmetric spaces naturally appear in many mathematical theories, including analysis (representation theory, nonabelian harmonic analysis), number theory (automorphic forms), algebraic geometry (modulae) and algebraic topology (cohomology of discrete groups). In most applications it is necessary to form an appropriate compactification of the space. The literature dealing with such compactifications is vast. The main purpose of this book is to introduce uniform constructions of most of the known compactifications with emphasis on their geometric and topological structures. The book is divided into three parts. Part I studies compactifications of Riemannian symmetric spaces and their arithmetic quotients. Part II is a study of compact smooth manifolds. Part III studies the compactification of locally symmetric spaces. Familiarity with the theory of semisimple Lie groups is assumed, as is familiarity with algebraic groups defined over the rational numbers in later parts of the book, although most of the pertinent material is recalled as presented. Otherwise, the book is a selfcontained reference aimed at graduate students and research mathematicians interested in the applications of Lie theory and representation theory to diverse fields of mathematics
Arithmetic groups and their generalizations : what, why, and how by
Lizhen Ji(
Book
)
9 editions published between 2008 and 2010 in English and held by 198 WorldCat member libraries worldwide
In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as \mathbf{Z} or \mathrm{SL}(n,\mathbf{Z}). Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields
9 editions published between 2008 and 2010 in English and held by 198 WorldCat member libraries worldwide
In one guise or another, many mathematicians are familiar with certain arithmetic groups, such as \mathbf{Z} or \mathrm{SL}(n,\mathbf{Z}). Yet, many applications of arithmetic groups and many connections to other subjects within mathematics are less well known. Indeed, arithmetic groups admit many natural and important generalizations. The purpose of this expository book is to explain, through some brief and informal comments and extensive references, what arithmetic groups and their generalizations are, why they are important to study, and how they can be understood and applied to many fields
Lie groups and automorphic forms : proceedings of the 2003 summer program, Zhejiang University, Center of Mathematical Sciences,
Hangzhou, China by
Lizhen Ji(
Book
)
8 editions published in 2006 in English and held by 147 WorldCat member libraries worldwide
Lie groups are fundamental objects in mathematics. They occur naturally in differential geometry, algebraic geometry, representation theory, number theory, and other areas. Closely related are arithmetic subgroups, locally symmetric spaces and the spectral theory of automorphic forms. This book consists of five chapters which give comprehensive introductions to Lie groups, Lie algebras, arithmetic groups and reduction theories, cohomology of arithmetic groups, and the Petersson and Kuznetsov trace formulas
8 editions published in 2006 in English and held by 147 WorldCat member libraries worldwide
Lie groups are fundamental objects in mathematics. They occur naturally in differential geometry, algebraic geometry, representation theory, number theory, and other areas. Closely related are arithmetic subgroups, locally symmetric spaces and the spectral theory of automorphic forms. This book consists of five chapters which give comprehensive introductions to Lie groups, Lie algebras, arithmetic groups and reduction theories, cohomology of arithmetic groups, and the Petersson and Kuznetsov trace formulas
Geometry of Riemann surfaces and their moduli spaces(
Book
)
8 editions published in 2009 in English and held by 114 WorldCat member libraries worldwide
8 editions published in 2009 in English and held by 114 WorldCat member libraries worldwide
Handbook of geometric analysis(
Book
)
in English and held by 103 WorldCat member libraries worldwide
in English and held by 103 WorldCat member libraries worldwide
Cohomology of groups and algebraic ktheory(
Book
)
7 editions published between 2009 and 2010 in English and held by 96 WorldCat member libraries worldwide
Cohomology of groups is a fundamental tool in many subjects of modern mathematics. One important generalized cohomology theory is the algebraic Ktheory. Indeed, algebraic Kgroups of rings are important invariants of the rings and have played important roles in algebra, topology, number theory, etc. This volume consists of expanded lecture notes from a 2007 seminar at Zhejiang University in China, at which several leading experts presented introductions, to and surveys of, many aspects of cohomology of groups and algebraic Ktheory, along with their broad applications. Two foundational papers on algebraic Ktheory by Daniel Quillen are also included. Book Jacket
7 editions published between 2009 and 2010 in English and held by 96 WorldCat member libraries worldwide
Cohomology of groups is a fundamental tool in many subjects of modern mathematics. One important generalized cohomology theory is the algebraic Ktheory. Indeed, algebraic Kgroups of rings are important invariants of the rings and have played important roles in algebra, topology, number theory, etc. This volume consists of expanded lecture notes from a 2007 seminar at Zhejiang University in China, at which several leading experts presented introductions, to and surveys of, many aspects of cohomology of groups and algebraic Ktheory, along with their broad applications. Two foundational papers on algebraic Ktheory by Daniel Quillen are also included. Book Jacket
Automorphic forms and the Langlands program(
Book
)
6 editions published between 2009 and 2010 in English and held by 93 WorldCat member libraries worldwide
6 editions published between 2009 and 2010 in English and held by 93 WorldCat member libraries worldwide
Sophus Lie and Felix Klein : the Erlangen program and its impact in mathematics and physics by
Lizhen Ji(
Book
)
10 editions published between 2014 and 2015 in English and held by 85 WorldCat member libraries worldwide
The Erlangen program expresses a fundamental point of view on the use of groups and transformation groups in mathematics and physics. The present volume is the first modern comprehensive book on that program and its impact in contemporary mathematics and physics. Klein spelled out the program, and Lie, who contributed to its formulation, is the first mathematician who made it effective in his work. The theories that these two authors developed are also linked to their personal history and to their relations with each other and with other mathematicians, incuding Hermann Weyl, Élie Cartan, Henri Poincaré, and many others. All these facets of the Erlangen program appear in the present volume. The book is written by wellknown experts in geometry, physics and history of mathematics and physics. It is addressed to mathematicians, to graduate students, and to all those interested in the development of mathematical ideas
10 editions published between 2014 and 2015 in English and held by 85 WorldCat member libraries worldwide
The Erlangen program expresses a fundamental point of view on the use of groups and transformation groups in mathematics and physics. The present volume is the first modern comprehensive book on that program and its impact in contemporary mathematics and physics. Klein spelled out the program, and Lie, who contributed to its formulation, is the first mathematician who made it effective in his work. The theories that these two authors developed are also linked to their personal history and to their relations with each other and with other mathematicians, incuding Hermann Weyl, Élie Cartan, Henri Poincaré, and many others. All these facets of the Erlangen program appear in the present volume. The book is written by wellknown experts in geometry, physics and history of mathematics and physics. It is addressed to mathematicians, to graduate students, and to all those interested in the development of mathematical ideas
Fifth International Congress of Chinese Mathematicians by
Lizhen Ji(
Book
)
8 editions published in 2012 in English and held by 74 WorldCat member libraries worldwide
This twopart volume represents the proceedings of the Fifth International Congress of Chinese Mathematicians, held at Tsinghua University, Beijing, in December 2010. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Included are 60 papers based on lectures given at the conference
8 editions published in 2012 in English and held by 74 WorldCat member libraries worldwide
This twopart volume represents the proceedings of the Fifth International Congress of Chinese Mathematicians, held at Tsinghua University, Beijing, in December 2010. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Included are 60 papers based on lectures given at the conference
Fourth International Congress of Chinese Mathematicians by
Lizhen Ji(
Book
)
6 editions published in 2010 in English and Undetermined and held by 67 WorldCat member libraries worldwide
This volume represents selected proceedings of the Fourth International Congress of Chinese Mathematicians, held in Hangzhou. China. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Approximately fifteen hundred mathematicians participated in the Congress
6 editions published in 2010 in English and Undetermined and held by 67 WorldCat member libraries worldwide
This volume represents selected proceedings of the Fourth International Congress of Chinese Mathematicians, held in Hangzhou. China. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Approximately fifteen hundred mathematicians participated in the Congress
Geometry, analysis and topology of discrete groups by Topology and Analysis of Locally Symmetric Spaces and Discrete Groups" Conference "Geometry(
Book
)
9 editions published in 2008 in English and held by 47 WorldCat member libraries worldwide
9 editions published in 2008 in English and held by 47 WorldCat member libraries worldwide
Great mathematics books of the twentieth century : a personal journey by
Lizhen Ji(
Book
)
6 editions published between 2013 and 2014 in English and held by 43 WorldCat member libraries worldwide
6 editions published between 2013 and 2014 in English and held by 43 WorldCat member libraries worldwide
Selected expository works of Shingtung Yau with commentary by
ShingTung Yau(
Book
)
2 editions published in 2014 in English and held by 43 WorldCat member libraries worldwide
2 editions published in 2014 in English and held by 43 WorldCat member libraries worldwide
Surveys in differential geometry : geometry of riemann surfaces and their moduli spaces(
Book
)
5 editions published in 2009 in English and held by 39 WorldCat member libraries worldwide
5 editions published in 2009 in English and held by 39 WorldCat member libraries worldwide
Transformation groups and moduli spaces of curves(
Book
)
6 editions published between 2010 and 2011 in English and held by 36 WorldCat member libraries worldwide
6 editions published between 2010 and 2011 in English and held by 36 WorldCat member libraries worldwide
The legacy of Bernhard Riemann after one hundred and fifty years(
Book
)
2 editions published in 2016 in English and held by 34 WorldCat member libraries worldwide
2 editions published in 2016 in English and held by 34 WorldCat member libraries worldwide
Open problems and surveys of contemporary mathematics(
Book
)
6 editions published in 2013 in English and held by 22 WorldCat member libraries worldwide
6 editions published in 2013 in English and held by 22 WorldCat member libraries worldwide
Handbook of geometric analysis by
Lizhen Lin(
Book
)
9 editions published in 2008 in English and Spanish and held by 20 WorldCat member libraries worldwide
9 editions published in 2008 in English and Spanish and held by 20 WorldCat member libraries worldwide
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Audience Level
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Related Identities
 Borel, Armand Author Dedicatee
 Yau, ShingTung 1949 Author Editor
 Guivarc'h, Y. Author
 Taylor, J. C. (John Christopher) 1936
 Liu, Kefeng 1965 Editor
 Wolpert, Scott A. Editor
 Papadopoulos, Athanase Editor
 Langlands, Robert P. 1936
 Klein, Felix 18491925
 Lie, Sophus 18421899
Useful Links
Associated Subjects
Algebraic number theory Algebraic topology Arithmetic groups Automorphic forms Cohomology operations Compactifications Curves, Algebraic Differential equations, Partial Discrete geometry Discrete groups Geometric analysis Geometric group theory Geometry Geometry, Algebraic Geometry, Differential Geometry, Projective Group actions (Mathematics) Group theory Homotopy groups Klein, Felix, Ktheory Langlands, Robert P., Lie, Sophus, Lie groups Linear algebraic groups Mathematical physics Mathematicians Mathematics MathematicsStudy and teaching (Higher) Moduli theory Number theory Representations of groups Representations of Lie groups Riemann, Bernhard, Riemann hypothesis Riemann surfaces Surfaces, Algebraic Symmetric spaces Topological groups Topology Transformation groups United States Yau, ShingTung,