Sarnak, Peter
Overview
Works:  66 works in 220 publications in 3 languages and 5,021 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other, Opponent, 958 
Classifications:  QA243, 511.5 
Publication Timeline
.
Most widely held works by
Peter Sarnak
Some applications of modular forms by
Peter Sarnak(
Book
)
25 editions published between 1989 and 2010 in English and Russian and held by 415 WorldCat member libraries worldwide
The theory of modular forms and especially the socalled 'Ramanujan conjectures' have been applied to resolve problems in combinatorics, computer science, analysis and number theory. This tract, based on the Wittemore Lectures given at Yale University, is concerned with describing some of these applications
25 editions published between 1989 and 2010 in English and Russian and held by 415 WorldCat member libraries worldwide
The theory of modular forms and especially the socalled 'Ramanujan conjectures' have been applied to resolve problems in combinatorics, computer science, analysis and number theory. This tract, based on the Wittemore Lectures given at Yale University, is concerned with describing some of these applications
Elementary number theory, group theory, and Ramanujan graphs by
Giuliana P Davidoff(
Book
)
19 editions published in 2003 in English and German and held by 394 WorldCat member libraries worldwide
This text is a self contained treatment of expander graphs and in particular their explicit construction. Expander graphs are both highly connected but sparse, and besides their interest within combinatorics and graph theory, they also find various applications in computer science and engineering. The reader needs only a background in elementary algebra, analysis and combinatorics; the authors supply the necessary background material from graph theory, number theory, group theory and representation theory. The text can therefore be used as a brief introduction to these subjects as well as an illustration of how such topics are synthesised in modern mathematics
19 editions published in 2003 in English and German and held by 394 WorldCat member libraries worldwide
This text is a self contained treatment of expander graphs and in particular their explicit construction. Expander graphs are both highly connected but sparse, and besides their interest within combinatorics and graph theory, they also find various applications in computer science and engineering. The reader needs only a background in elementary algebra, analysis and combinatorics; the authors supply the necessary background material from graph theory, number theory, group theory and representation theory. The text can therefore be used as a brief introduction to these subjects as well as an illustration of how such topics are synthesised in modern mathematics
Random matrices, Frobenius eigenvalues, and monodromy by
Nicholas M Katz(
Book
)
14 editions published between 1998 and 1999 in English and held by 385 WorldCat member libraries worldwide
The main topic of this book is the deep relation between the spacings between zeros of zeta and Lfunctions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the MontgomeryOdlyzko law, is shown to hold for wide classes of zeta and Lfunctions over finite fields. The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinit
14 editions published between 1998 and 1999 in English and held by 385 WorldCat member libraries worldwide
The main topic of this book is the deep relation between the spacings between zeros of zeta and Lfunctions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the MontgomeryOdlyzko law, is shown to hold for wide classes of zeta and Lfunctions over finite fields. The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinit
The Selberg trace formula and related topics : proceedings of the AMSIMSSIAM Joint Summer Research Conference held July
2228, 1984 with support from the National Science Foundation by
Brunswick, Me.> Joint Summer Research Conference in the Mathematical Sciences on the Selberg Trace Formula and Related Topics <1984(
Book
)
11 editions published in 1986 in English and held by 252 WorldCat member libraries worldwide
11 editions published in 1986 in English and held by 252 WorldCat member libraries worldwide
Extremal Riemann surfaces by
J. R Quine(
Book
)
14 editions published between 1996 and 1997 in English and held by 223 WorldCat member libraries worldwide
This volume is an outgrowth of the AMS Special Session on Extremal Riemann Surfaces held at the Joint Mathematics Meeting in San Francisco, January 1995. The book deals with a variety of extremal problems related to Riemann surfaces. Some papers deal with the identification of surfaces with longest systole (element of shortest nonzero length) for the length spectrum and the Jacobian. Parallels are drawn to classical questions involving extremal lattices. Other papers deal with maximizing or minimizing functions defined by the spectrum such as the heat kernel, the zeta function, and the determinant of the Laplacian, some from the point of view of identifying an extremal metric
14 editions published between 1996 and 1997 in English and held by 223 WorldCat member libraries worldwide
This volume is an outgrowth of the AMS Special Session on Extremal Riemann Surfaces held at the Joint Mathematics Meeting in San Francisco, January 1995. The book deals with a variety of extremal problems related to Riemann surfaces. Some papers deal with the identification of surfaces with longest systole (element of shortest nonzero length) for the length spectrum and the Jacobian. Parallels are drawn to classical questions involving extremal lattices. Other papers deal with maximizing or minimizing functions defined by the spectrum such as the heat kernel, the zeta function, and the determinant of the Laplacian, some from the point of view of identifying an extremal metric
Automorphic forms and applications(
Book
)
5 editions published in 2007 in English and held by 179 WorldCat member libraries worldwide
"The theory of automorphic forms has seen dramatic developments in recent years. In particular, important instances of Langlands functoriality have been established. This volume presents three weeks of lectures from the IAS/Park City Mathematics Institute Summer School on automorphic forms and their applications. It addresses some of the general aspects of automorphic forms, as well as certain recent advances in the field." "This volume is recommended for independent study or an advanced topics course. It is suitable for graduate students and researchers interested in automorphic forms and number theory."Jacket
5 editions published in 2007 in English and held by 179 WorldCat member libraries worldwide
"The theory of automorphic forms has seen dramatic developments in recent years. In particular, important instances of Langlands functoriality have been established. This volume presents three weeks of lectures from the IAS/Park City Mathematics Institute Summer School on automorphic forms and their applications. It addresses some of the general aspects of automorphic forms, as well as certain recent advances in the field." "This volume is recommended for independent study or an advanced topics course. It is suitable for graduate students and researchers interested in automorphic forms and number theory."Jacket
Selected papers by
Peter D Lax(
Book
)
12 editions published between 2004 and 2013 in English and Undetermined and held by 148 WorldCat member libraries worldwide
12 editions published between 2004 and 2013 in English and Undetermined and held by 148 WorldCat member libraries worldwide
Selected works of Ilya PiatetskiShapiro by
I. I Pi︠a︡tet︠s︡kiĭShapiro(
Book
)
6 editions published between 2000 and 2001 in English and held by 136 WorldCat member libraries worldwide
6 editions published between 2000 and 2001 in English and held by 136 WorldCat member libraries worldwide
Festschrift in honor of I.I. PiatetskiShapiro on the occasion of his sixtieth birthday by
Stephen S Gelbart(
Book
)
6 editions published in 1990 in English and held by 78 WorldCat member libraries worldwide
6 editions published in 1990 in English and held by 78 WorldCat member libraries worldwide
Selected papers by
Peter D Lax(
Book
)
14 editions published in 2005 in English and held by 27 WorldCat member libraries worldwide
A renowned mathematician who considers himself both applied and theoretical in his approach, the author has spent most of his professional career at NYU, making significant contributions to both mathematics and computing. He has written several published works and has received numerous honors
14 editions published in 2005 in English and held by 27 WorldCat member libraries worldwide
A renowned mathematician who considers himself both applied and theoretical in his approach, the author has spent most of his professional career at NYU, making significant contributions to both mathematics and computing. He has written several published works and has received numerous honors
Selected papers by
Peter D Lax(
Book
)
12 editions published in 2005 in English and held by 15 WorldCat member libraries worldwide
A renowned mathematician who considers himself both applied and theoretical in his approach, Peter Lax has spent most of his professional career at NYU, making significant contributions to both mathematics and computing. He has written several important published works and has received numerous honours including the National Medal of Science, the Lester R. Ford Award, the Chauvenet Prize, the Semmelweis Medal, the Wiener Prize, and the Wolf Prize. Several students he has mentored have become leaders in their fields. These two volumes span the years from 1952 up until 1999, and cover many varying topics, from functional analysis, partial differential equations, and numerical methods to conservation laws, integrable systems and scattering theory. After each paper, or collection of papers, is a commentary placing the paper in context and where relevant discussing more recent developments. Many of the papers in these volumes have become classics and should be read by any serious student of these topics. In terms of insight, depth, and breadth, Lax has few equals. The reader of this selection will quickly appreciate his brilliance as well as his masterful touch. Having this collection of papers in one place allows one to follow the evolution of his ideas and mathematical interests and to appreciate how many of these papers initiated topics that developed lives of their own
12 editions published in 2005 in English and held by 15 WorldCat member libraries worldwide
A renowned mathematician who considers himself both applied and theoretical in his approach, Peter Lax has spent most of his professional career at NYU, making significant contributions to both mathematics and computing. He has written several important published works and has received numerous honours including the National Medal of Science, the Lester R. Ford Award, the Chauvenet Prize, the Semmelweis Medal, the Wiener Prize, and the Wolf Prize. Several students he has mentored have become leaders in their fields. These two volumes span the years from 1952 up until 1999, and cover many varying topics, from functional analysis, partial differential equations, and numerical methods to conservation laws, integrable systems and scattering theory. After each paper, or collection of papers, is a commentary placing the paper in context and where relevant discussing more recent developments. Many of the papers in these volumes have become classics and should be read by any serious student of these topics. In terms of insight, depth, and breadth, Lax has few equals. The reader of this selection will quickly appreciate his brilliance as well as his masterful touch. Having this collection of papers in one place allows one to follow the evolution of his ideas and mathematical interests and to appreciate how many of these papers initiated topics that developed lives of their own
Selected papers by
Peter D Lax(
Book
)
5 editions published in 2005 in English and held by 15 WorldCat member libraries worldwide
5 editions published in 2005 in English and held by 15 WorldCat member libraries worldwide
The word and riemannian metrics on lattices of semisimple groups by
Alexander Lubotzky(
Book
)
3 editions published between 2000 and 2001 in English and held by 12 WorldCat member libraries worldwide
3 editions published between 2000 and 2001 in English and held by 12 WorldCat member libraries worldwide
The Schur lectures (1992) by
Roger Howe(
Book
)
3 editions published in 1995 in English and held by 10 WorldCat member libraries worldwide
3 editions published in 1995 in English and held by 10 WorldCat member libraries worldwide
Set theory by
George J Tourlakis(
)
1 edition published in 2003 in English and held by 0 WorldCat member libraries worldwide
This twovolume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a userfriendly conversational lecture style that makes them equally effective for selfstudy or class use. Volume II, on formal (ZFC) set theory, incorporates a selfcontained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing
1 edition published in 2003 in English and held by 0 WorldCat member libraries worldwide
This twovolume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a userfriendly conversational lecture style that makes them equally effective for selfstudy or class use. Volume II, on formal (ZFC) set theory, incorporates a selfcontained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing
Harmonic Maps, Conservation Laws and Moving Frames by
Béla Bollobás(
)
2 editions published in 2002 in English and held by 0 WorldCat member libraries worldwide
Annotation This accessible introduction to harmonic map theory and its analytical aspects, covers recent developments in the regularity theory of weakly harmonic maps. The book begins by introducing these concepts, stressing the interplay between geometry, the role of symmetries and weak solutions. It then presents a guided tour into the theory of completely integrable systems for harmonic maps, followed by two chapters devoted to recent results on the regularity of weak solutions. A presentation of "exotic" functional spaces from the theory of harmonic analysis is given and these tools are then used for proving regularity results. The importance of conservation laws is stressed and the concept of a "Coulomb moving frame" is explained in detail. The book ends with further applications and illustrations of Coulomb moving frames to the theory of surfaces
2 editions published in 2002 in English and held by 0 WorldCat member libraries worldwide
Annotation This accessible introduction to harmonic map theory and its analytical aspects, covers recent developments in the regularity theory of weakly harmonic maps. The book begins by introducing these concepts, stressing the interplay between geometry, the role of symmetries and weak solutions. It then presents a guided tour into the theory of completely integrable systems for harmonic maps, followed by two chapters devoted to recent results on the regularity of weak solutions. A presentation of "exotic" functional spaces from the theory of harmonic analysis is given and these tools are then used for proving regularity results. The importance of conservation laws is stressed and the concept of a "Coulomb moving frame" is explained in detail. The book ends with further applications and illustrations of Coulomb moving frames to the theory of surfaces
Fixed point theory and applications by
Ravi P Agarwal(
)
1 edition published in 2001 in English and held by 0 WorldCat member libraries worldwide
Annotation This clear exposition of the flourishing field of fixed point theory, an important tool in the fields of differential equations and functional equations, starts from the basics of Banach's contraction theorem and develops most of the main results and techniques. The book explores many applications of the theory to analysis, with topological considerations playing a crucial role. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type
1 edition published in 2001 in English and held by 0 WorldCat member libraries worldwide
Annotation This clear exposition of the flourishing field of fixed point theory, an important tool in the fields of differential equations and functional equations, starts from the basics of Banach's contraction theorem and develops most of the main results and techniques. The book explores many applications of the theory to analysis, with topological considerations playing a crucial role. The very extensive bibliography and close to 100 exercises mean that it can be used both as a text and as a comprehensive reference work, currently the only one of its type
Floer Homology Groups in YangMills Theory by
S. K Donaldson(
)
1 edition published in 2002 in English and held by 0 WorldCat member libraries worldwide
Annotation This monograph gives a thorough exposition of Floer's seminal work during the 1980s from a contemporary viewpoint. The material contained here was developed with specific applications in mind. However, it has now become clear that the techniques used are important for many current areas of research. An important example would be symplectic theory and gluing problems for selfdual metrics and other metrics with special holonomy. The author writes with the big picture constantly in mind. As well as a review of the current state of knowledge, there are sections on the likely direction of future research. Included in this are connections between Floer groups and the celebrated SeibergWitten invariants. The results described in this volume form part of the area known as Donaldson theory. The significance of this work is such that the author was awarded the prestigious Fields Medal for his contribution
1 edition published in 2002 in English and held by 0 WorldCat member libraries worldwide
Annotation This monograph gives a thorough exposition of Floer's seminal work during the 1980s from a contemporary viewpoint. The material contained here was developed with specific applications in mind. However, it has now become clear that the techniques used are important for many current areas of research. An important example would be symplectic theory and gluing problems for selfdual metrics and other metrics with special holonomy. The author writes with the big picture constantly in mind. As well as a review of the current state of knowledge, there are sections on the likely direction of future research. Included in this are connections between Floer groups and the celebrated SeibergWitten invariants. The results described in this volume form part of the area known as Donaldson theory. The significance of this work is such that the author was awarded the prestigious Fields Medal for his contribution
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Related Identities
 Davidoff, Giuliana P. Author
 Valette, Alain
 Lax, Peter D. Author
 Majda, Andrew 1949 Author Editor
 Bollobas, B. Other Editor
 Fulton, W. Other Editor
 Kirwan, F. Other Editor
 Katok, A. Other Editor
 Katz, Nicholas M. 1943 Author
 Hejhal, Dennis A. Other Author Editor
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Associated Subjects
Arithmetical algebraic geometry Automorphic forms Automorphic functions Complex manifolds Differentiable dynamical systems Differential equations Differential equations, Partial Eigenvalues Extremal problems (Mathematics) Fixed point theory Forms, Modular Forms (Mathematics) Functional equations Functions, Zeta Geometry, Differential Global analysis (Mathematics) Graph theory Group actions (Mathematics) Group theory Hamiltonian systems Harmonic analysis Harmonic maps Invariants Lax, Peter D Lfunctions Limit theorems (Probability theory) Logic, Symbolic and mathematical Mappings (Mathematics) Mathematicians Mathematics MathematicsStudy and teaching Matrices Monodromy groups Number theory Pi︠a︡tet︠s︡kiĭShapiro, I. I.(Ilʹi︠a︡ Iosifovich), Quantum chaos Random matrices Representations of groups Riemannian manifolds Riemann surfaces Selberg trace formula Set theory United States YangMills theory
Alternative Names
Peter Sarnak Amerikaans wiskundige
Peter Sarnak amerikanischer Mathematiker
Peter Sarnak amerikansk matematikar
Peter Sarnak amerikansk matematiker
Peter Sarnak matemático sudafricano
Peter Sarnak mathématicien sudaméricain naturalisé américain.
Sarnak, P.
Sarnak, P. 1953
Sarnak, P. (Peter)
Питер Сарнак
Пітер Сарнак
פיטר סרנק
פיטר סרנק מתמטיקאי דרום אפריקאי
পিটার ক্লাইভ সারনাক
ピーター・サルナック
彼得·薩那克
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