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Action-minimizing Methods in Hamiltonian Dynamics (MN-50)An Introduction to Aubry-Mather Theory

Action-minimizing Methods in Hamiltonian Dynamics (MN-50): An Introduction to Aubry-Mather Theory

Alfonso Sorrentino

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691164502
eISBN:
9781400866618
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691164502.001.0001
Subject:
Mathematics, Applied Mathematics

John Mather's seminal works in Hamiltonian dynamics represent some of the most important contributions to our understanding of the complex balance between stable and unstable motions in classical ... More

Advances in AnalysisThe Legacy of Elias M. Stein

Advances in Analysis: The Legacy of Elias M. Stein

Charles Fefferman, Alexandru D. Ionescu, D.H. Phong, and Stephen Wainger

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691159416
eISBN:
9781400848935
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691159416.001.0001
Subject:
Mathematics, Numerical Analysis

Princeton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory. His ... More

Agent_ZeroToward Neurocognitive Foundations for Generative Social Science

Agent_Zero: Toward Neurocognitive Foundations for Generative Social Science

Joshua M. Epstein

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691158884
eISBN:
9781400848256
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691158884.001.0001
Subject:
Mathematics, Applied Mathematics

This book introduces a new theoretical entity: Agent_Zero. This software individual, or “agent,” is endowed with distinct emotional/affective, cognitive/deliberative, and social modules. Grounded in ... More

The Ambient Metric (AM-178)

The Ambient Metric (AM-178)

Charles Fefferman and C. Robin Graham

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691153131
eISBN:
9781400840588
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153131.001.0001
Subject:
Mathematics, Geometry / Topology

This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient ... More

Arithmetic Compactifications of PEL-Type Shimura Varieties

Arithmetic Compactifications of PEL-Type Shimura Varieties

Kai-Wen Lan

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691156545
eISBN:
9781400846016
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691156545.001.0001
Subject:
Mathematics, Geometry / Topology

By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical ... More

Asymptotic Differential Algebra and Model Theory of Transseries

Asymptotic Differential Algebra and Model Theory of Transseries

Matthias Aschenbrenner, Lou van den Dries, and Joris van der Hoeven

Published in print:
2017
Published Online:
October 2017
ISBN:
9780691175423
eISBN:
9781400885411
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175423.001.0001
Subject:
Mathematics, Computational Mathematics / Optimization

Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a ... More

Benford's LawTheory and Applications

Benford's Law: Theory and Applications

Steven J. Miller (ed.)

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691147611
eISBN:
9781400866595
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691147611.001.0001
Subject:
Mathematics, Probability / Statistics

Benford's law states that the leading digits of many data sets are not uniformly distributed from one through nine, but rather exhibit a profound bias. This bias is evident in everything from ... More

Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

Chow Rings, Decomposition of the Diagonal, and the Topology of Families (AM-187)

Claire Voisin

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691160504
eISBN:
9781400850532
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691160504.001.0001
Subject:
Mathematics, Geometry / Topology

This book provides an introduction to algebraic cycles on complex algebraic varieties, to the major conjectures relating them to cohomology, and even more precisely to Hodge structures on cohomology. ... More

Circles DisturbedThe Interplay of Mathematics and Narrative

Circles Disturbed: The Interplay of Mathematics and Narrative

Apostolos Doxiadis and Barry Mazur (eds)

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691149042
eISBN:
9781400842681
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691149042.001.0001
Subject:
Mathematics, History of Mathematics

This book brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. “Circles disturbed” reflect the last words of ... More

Classification of Pseudo-reductive Groups (AM-191)

Classification of Pseudo-reductive Groups (AM-191)

Brian Conrad and Gopal Prasad

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691167923
eISBN:
9781400874026
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691167923.001.0001
Subject:
Mathematics, Numerical Analysis

This book goes further than the exploration of the general structure of pseudo-reductive groups to study the classification over an arbitrary field. An Isomorphism Theorem proved here determines the ... More

Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Complex Ball Quotients and Line Arrangements in the Projective Plane (MN-51)

Paula Tretkoff

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691144771
eISBN:
9781400881253
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691144771.001.0001
Subject:
Mathematics, Geometry / Topology

This book introduces the theory of complex surfaces through a comprehensive look at finite covers of the projective plane branched along line arrangements. It emphasizes those finite coverings that ... More

Computational Aspects of Modular Forms and Galois RepresentationsHow One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176)

Computational Aspects of Modular Forms and Galois Representations: How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176)

Bas Edixhoven and Jean-Marc Couveignes (eds)

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691142012
eISBN:
9781400839001
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691142012.001.0001
Subject:
Mathematics, Number Theory

Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's ... More

Convolution and EquidistributionSato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180)

Nicholas M. Katz

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153308
eISBN:
9781400842704
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153308.001.0001
Subject:
Mathematics, Number Theory

This book explores an important aspect of number theory—the theory of exponential sums over finite fields and their Mellin transforms—from a new, categorical point of view. The book presents ... More

The Decomposition of Global Conformal Invariants (AM-182)

The Decomposition of Global Conformal Invariants (AM-182)

Spyros Alexakis

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153476
eISBN:
9781400842728
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153476.001.0001
Subject:
Mathematics, Geometry / Topology

This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question ... More

Degenerate Diffusion Operators Arising in Population Biology (AM-185)

Degenerate Diffusion Operators Arising in Population Biology (AM-185)

Charles L. Epstein and Rafe Mazzeo

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691157122
eISBN:
9781400846108
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691157122.001.0001
Subject:
Mathematics, Probability / Statistics

This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as ... More

Descent in Buildings (AM-190)

Descent in Buildings (AM-190)

Bernhard Mühlherr, Holger P. Petersson, and Richard M. Weiss

Published in print:
2015
Published Online:
October 2017
ISBN:
9780691166902
eISBN:
9781400874019
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691166902.001.0001
Subject:
Mathematics, Combinatorics / Graph Theory / Discrete Mathematics

This book begins with the resolution of a major open question about the local structure of Bruhat-Tits buildings. It then puts forward an algebraic solution into a geometric context by developing a ... More

Enlightening SymbolsA Short History of Mathematical Notation and Its Hidden Powers

Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers

Joseph Mazur

Published in print:
2016
Published Online:
January 2018
ISBN:
9780691173375
eISBN:
9781400850112
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691173375.001.0001
Subject:
Mathematics, History of Mathematics

While all of us regularly use basic mathematical symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did ... More

The Fascinating World of Graph Theory

The Fascinating World of Graph Theory

Ping Zhang, Gary Chartrand, and Arthur Benjamin

Published in print:
2017
Published Online:
May 2018
ISBN:
9780691175638
eISBN:
9781400852000
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691175638.001.0001
Subject:
Mathematics, Applied Mathematics

Graph theory goes back several centuries and revolves around the study of graphs—mathematical structures showing relations between objects. With applications in biology, computer science, ... More

Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)

Isroil A. Ikromov and Detlef Müller

Published in print:
2016
Published Online:
October 2017
ISBN:
9780691170541
eISBN:
9781400881246
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691170541.001.0001
Subject:
Mathematics, Geometry / Topology

This is the first book to present a complete characterization of Stein–Tomas-type Fourier restriction estimates for large classes of smooth hypersurfaces in three dimensions, including all ... More

Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)

Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces (AM-179)

Joram Lindenstrauss, David Preiss, and Jaroslav Tier

Published in print:
2012
Published Online:
October 2017
ISBN:
9780691153551
eISBN:
9781400842698
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691153551.001.0001
Subject:
Mathematics, Analysis

This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the ... More

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