Ji, Lizhen 1964
Overview
Works:  126 works in 350 publications in 2 languages and 3,176 library holdings 

Genres:  Conference papers and proceedings History Bibliography 
Roles:  Editor, Author, Other, Dedicatee, Contributor 
Publication Timeline
.
Most widely held works by
Lizhen Ji
Compactifications of symmetric and locally symmetric spaces by
Armand Borel(
)
22 editions published between 2006 and 2008 in English and held by 644 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 644 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
Compactifications of symmetric spaces by
Y Guivarc'h(
Book
)
14 editions published between 1996 and 1998 in English and held by 347 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
14 editions published between 1996 and 1998 in English and held by 347 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
Arithmetic groups and their generalizations : what, why, and how by
Lizhen Ji(
Book
)
11 editions published between 2008 and 2010 in English and held by 223 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
11 editions published between 2008 and 2010 in English and held by 223 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
From Riemann to differential geometry and relativity(
)
7 editions published in 2017 in English and German and held by 218 WorldCat member libraries worldwide
This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann's ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann's work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.
7 editions published in 2017 in English and German and held by 218 WorldCat member libraries worldwide
This book explores the work of Bernhard Riemann and its impact on mathematics, philosophy and physics. It features contributions from a range of fields, historical expositions, and selected research articles that were motivated by Riemann's ideas and demonstrate their timelessness. The editors are convinced of the tremendous value of going into Riemann's work in depth, investigating his original ideas, integrating them into a broader perspective, and establishing ties with modern science and philosophy. Accordingly, the contributors to this volume are mathematicians, physicists, philosophers and historians of science. The book offers a unique resource for students and researchers in the fields of mathematics, physics and philosophy, historians of science, and more generally to a wide range of readers interested in the history of ideas.
Lie groups and automorphic forms : proceedings of the 2003 summer program, Zhejiang University, Center of Mathematical Sciences,
Hangzhou, China by
Lizhen Ji(
Book
)
9 editions published in 2006 in English and held by 175 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
9 editions published in 2006 in English and held by 175 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 126 WorldCat member libraries worldwide
8 editions published in 2009 in English and held by 126 WorldCat member libraries worldwide
Sophus Lie and Felix Klein : the Erlangen program and its impact in mathematics and physics by
Lizhen Ji(
Book
)
11 editions published in 2015 in English and held by 124 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
11 editions published in 2015 in English and held by 124 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
Handbook of geometric analysis(
Book
)
6 editions published between 2008 and 2010 in English and held by 114 WorldCat member libraries worldwide
6 editions published between 2008 and 2010 in English and held by 114 WorldCat member libraries worldwide
Cohomology of groups and algebraic ktheory(
Book
)
7 editions published between 2009 and 2010 in English and held by 100 WorldCat member libraries worldwide
Published jointly by International Press and by Higher Education Press of China, the Advanced Lectures in Mathematics (ALM) series brings the latest mathematical developments worldwide to both researchers and students. Each volume consists of either an expository monograph or a collection of significant introductions to important topics. The ALM series emphasizes discussion of the history and significance of each topic discussed, with an overview of the current status of research, and presentation of the newest cuttingedge results
7 editions published between 2009 and 2010 in English and held by 100 WorldCat member libraries worldwide
Published jointly by International Press and by Higher Education Press of China, the Advanced Lectures in Mathematics (ALM) series brings the latest mathematical developments worldwide to both researchers and students. Each volume consists of either an expository monograph or a collection of significant introductions to important topics. The ALM series emphasizes discussion of the history and significance of each topic discussed, with an overview of the current status of research, and presentation of the newest cuttingedge results
Automorphic forms and the Langlands program(
Book
)
7 editions published between 2009 and 2010 in English and held by 98 WorldCat member libraries worldwide
Published jointly by International Press and by Higher Education Press of China, the Advanced Lectures in Mathematics (ALM) series brings the latest mathematical developments worldwide to both researchers and students. Each volume consists of either an expository monograph or a collection of significant introductions to important topics. The ALM series emphasizes discussion of the history and significance of each topic discussed, with an overview of the current status of research, and presentation of the newest cuttingedge results.<BR><BR>Classical modular forms on the upper half plane, with respect to the modular group SL(2, Z) and its congruence subgroups, have arisen naturally in number theory, complex analysis, topology, mathematical physics, and many other subjects. The closely related automorphic representations are basic notions in the celebrated Langlands program, which was proposed by Langlands in the late 1960s and has since revolutionized the fields of number theory, arithmetic algebraic geometry, and representation theory. This volume consists of expanded lecture notes from a 2007 international conference in Guangzhou, China, at which several leading experts in number theory presented introductions to, and surveys of, many aspects of automorphic forms and the Langlands program. Book Jacket
7 editions published between 2009 and 2010 in English and held by 98 WorldCat member libraries worldwide
Published jointly by International Press and by Higher Education Press of China, the Advanced Lectures in Mathematics (ALM) series brings the latest mathematical developments worldwide to both researchers and students. Each volume consists of either an expository monograph or a collection of significant introductions to important topics. The ALM series emphasizes discussion of the history and significance of each topic discussed, with an overview of the current status of research, and presentation of the newest cuttingedge results.<BR><BR>Classical modular forms on the upper half plane, with respect to the modular group SL(2, Z) and its congruence subgroups, have arisen naturally in number theory, complex analysis, topology, mathematical physics, and many other subjects. The closely related automorphic representations are basic notions in the celebrated Langlands program, which was proposed by Langlands in the late 1960s and has since revolutionized the fields of number theory, arithmetic algebraic geometry, and representation theory. This volume consists of expanded lecture notes from a 2007 international conference in Guangzhou, China, at which several leading experts in number theory presented introductions to, and surveys of, many aspects of automorphic forms and the Langlands program. Book Jacket
Fourth International Congress of Chinese Mathematicians by International Congress of Chinese Mathematicians(
Book
)
4 editions published in 2010 in English and held by 81 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
4 editions published in 2010 in English and held by 81 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
Fifth International Congress of Chinese Mathematicians by International Congress of Chinese Mathematicians(
Book
)
4 editions published in 2012 in English and held by 73 WorldCat member libraries worldwide
4 editions published in 2012 in English and held by 73 WorldCat member libraries worldwide
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 49 WorldCat member libraries worldwide
9 editions published in 2008 in English and held by 49 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 45 WorldCat member libraries worldwide
2 editions published in 2014 in English and held by 45 WorldCat member libraries worldwide
The legacy of Bernhard Riemann after one hundred and fifty years by
Lizhen Ji(
Book
)
6 editions published between 2015 and 2016 in English and held by 44 WorldCat member libraries worldwide
6 editions published between 2015 and 2016 in English and held by 44 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 44 WorldCat member libraries worldwide
6 editions published between 2013 and 2014 in English and held by 44 WorldCat member libraries worldwide
Transformation groups and moduli spaces of curves by Transformation groups and orbifolds(
Book
)
8 editions published between 2010 and 2011 in English and held by 42 WorldCat member libraries worldwide
8 editions published between 2010 and 2011 in English and held by 42 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 35 WorldCat member libraries worldwide
5 editions published in 2009 in English and held by 35 WorldCat member libraries worldwide
Fifth International Congress of Chinese Mathematicians by
Lizhen Ji(
)
5 editions published in 2012 in English and held by 34 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
5 editions published in 2012 in English and held by 34 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
Hodge theory and L²analysis by Hodge Theory and L2cohomology(
Book
)
4 editions published in 2017 in English and held by 31 WorldCat member libraries worldwide
4 editions published in 2017 in English and held by 31 WorldCat member libraries worldwide
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Related Identities
 Yau, ShingTung 1949 Honoree Author Editor
 Borel, Armand Author Dedicatee
 Papadopoulos, Athanase Other Editor
 Guivarc'h, Y. Author
 Taylor, J. C. (John Christopher) 1936
 Yamada, Sumio Other Editor
 Liu, Kefeng 1965 Editor
 Wolpert, Scott A. Editor
 Yang, Lo Editor
 Langlands, Robert P. 1936
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 theory History Hodge 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 Relativity (Physics) 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,
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Alternative Names
Ji, L. 1964
Ji, Lijin, 1964
Ji, Lizhen
Ji Lizhen 1964
Lizhen Ji.
Lizhen Ji 1964
Lizhen Ji Amerikaans wiskundige
Lizhen Ji matemático estadounidense
Lizhen Ji matematico statunitense
Lizhen Ji mathématicien américain
季, 理真 1964
季理真
季理真 1964
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