Sarnak, Peter
Overview
Works:  67 works in 214 publications in 3 languages and 4,787 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other, Opponent, 958 
Classifications:  QA243, 514 
Publication Timeline
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Most widely held works by
Peter Sarnak
Some applications of modular forms by
Peter Sarnak(
Book
)
24 editions published between 1989 and 2010 in English and Russian and held by 414 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
24 editions published between 1989 and 2010 in English and Russian and held by 414 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
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
Random matrices, Frobenius eigenvalues, and monodromy by
Nicholas M Katz(
Book
)
14 editions published between 1998 and 1999 in English and held by 386 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 386 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 AMSIMSSIAM Joint Summer Research Conference in the Mathematical Sciences on the Selberg Trace Formula and Related Topics(
Book
)
10 editions published in 1986 in English and held by 245 WorldCat member libraries worldwide
10 editions published in 1986 in English and held by 245 WorldCat member libraries worldwide
Extremal Riemann surfaces by
J. R Quine(
Book
)
15 editions published between 1996 and 2015 in English and held by 223 WorldCat member libraries worldwide
There are discussions of Hurwitz surfaces and surfaces with large cyclic groups of automorphisms. Also discussed are surfaces which are natural candidates for solving extremal problems such as triangular, modular, and arithmetic surfaces, and curves in various group theoretically defined curve families. Other allied topics are theta identities, quadratic periods of Abelian differentials, Teichmuller disks, binary quadratic forms, and spectral asymptotics of degenerating hyperbolic three manifolds
15 editions published between 1996 and 2015 in English and held by 223 WorldCat member libraries worldwide
There are discussions of Hurwitz surfaces and surfaces with large cyclic groups of automorphisms. Also discussed are surfaces which are natural candidates for solving extremal problems such as triangular, modular, and arithmetic surfaces, and curves in various group theoretically defined curve families. Other allied topics are theta identities, quadratic periods of Abelian differentials, Teichmuller disks, binary quadratic forms, and spectral asymptotics of degenerating hyperbolic three manifolds
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
)
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
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
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
Festschrift in honor of I.I. PiatetskiShapiro on the occasion of his sixtieth birthday(
Book
)
2 editions published in 1990 in English and held by 10 WorldCat member libraries worldwide
2 editions published in 1990 in English and held by 10 WorldCat member libraries worldwide
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
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
Typical dynamics of volume preserving homeomorphisms by
Steve Alpern(
)
3 editions published in 2001 in English and held by 0 WorldCat member libraries worldwide
This 2000 book provides a selfcontained introduction to typical properties of homeomorphisms. Examples of properties of homeomorphisms considered include transitivity, chaos and ergodicity. A key idea here is the interrelation between typical properties of volume preserving homeomorphisms and typical properties of volume preserving bijections of the underlying measure space. The authors make the first part of this book very concrete by considering volume preserving homeomorphisms of the unit ndimensional cube, and they go on to prove fixed point theorems (Conley & ndash;Zehnder & ndash; Franks). This is done in a number of short selfcontained chapters which would be suitable for an undergraduate analysis seminar or a graduate lecture course. Much of this work describes the work of the two authors, over the last twenty years, in extending to different settings and properties, the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property
3 editions published in 2001 in English and held by 0 WorldCat member libraries worldwide
This 2000 book provides a selfcontained introduction to typical properties of homeomorphisms. Examples of properties of homeomorphisms considered include transitivity, chaos and ergodicity. A key idea here is the interrelation between typical properties of volume preserving homeomorphisms and typical properties of volume preserving bijections of the underlying measure space. The authors make the first part of this book very concrete by considering volume preserving homeomorphisms of the unit ndimensional cube, and they go on to prove fixed point theorems (Conley & ndash;Zehnder & ndash; Franks). This is done in a number of short selfcontained chapters which would be suitable for an undergraduate analysis seminar or a graduate lecture course. Much of this work describes the work of the two authors, over the last twenty years, in extending to different settings and properties, the celebrated result of Oxtoby and Ulam that for volume homeomorphisms of the unit cube, ergodicity is a typical property
Lectures in Logic and Set Theory:. Set Theory by
George J Tourlakis(
)
1 edition published in 2003 in English and held by 0 WorldCat member libraries worldwide
Provides the reader with a solid foundation in set theory, while the inclusion of 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, will usher the advanced reader to the doorstep of the research literature
1 edition published in 2003 in English and held by 0 WorldCat member libraries worldwide
Provides the reader with a solid foundation in set theory, while the inclusion of 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, will usher the advanced reader to the doorstep of the research literature
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
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Related Identities
 Valette, Alain
 Davidoff, Giuliana P. Author
 Lax, Peter D. Author
 Majda, Andrew 1949 Author Editor
 Katz, Nicholas M. 1943 Author
 Katok, A. Other Editor
 Kirwan, F. Other Editor
 Fulton, W. Other Editor
 Bollobas, B. Other Editor
 Hejhal, Dennis A. Other 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 Ergodic theory Extremal problems (Mathematics) Fixed point theory Forms, Modular Forms (Mathematics) Functional equations Functions, Zeta Geometry Geometry, Differential Global analysis (Mathematics) Graph theory Group actions (Mathematics) Group theory Hamiltonian systems Harmonic analysis Harmonic maps Homeomorphisms Invariants Lax, Peter D Lfunctions Limit theorems (Probability theory) Logic, Symbolic and mathematical Mappings (Mathematics) Mathematicians Mathematics MathematicsStudy and teaching Matrices Measurepreserving transformations 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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