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VOLUME 54 NUMBER 4 OCTOBER 2017

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BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY

CONTENTS

Vol. 54, No. 4 October 2017

ARTICLES

Susan Friedlander, Introduction to the Tate issue . . . . . . . . . . . . . . . . . . . . . . . 541

J. S. Milne, The work of John Tate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544

John Tate, Number theory in the 20th century: Part 1 . . . . . . . . . . . . . . . . . . . 547

J. S. Milne, Review of the Collected Works of John Tate . . . . . . . . . . . . . . . . . 551

Pierre Colmez, Tate’s work and the Serre–Tate correspondence . . . . . . . . . . 559

Burt Totaro, Recent progress on the Tate conjecture . . . . . . . . . . . . . . . . . . . . 575

Joseph H. Silverman, Rational points on, and the arithmetic of, ellipticcurves: A tale of two books (and an article) . . . . . . . . . . . . . . . . . . . . . . . . . . 591

Herwig Hauser, The classical Artin approximation theorems . . . . . . . . . . . . 595

Alexander S. Merkurjev, Essential dimension . . . . . . . . . . . . . . . . . . . . . . . . . . 635

MATHEMATICAL PERSPECTIVES

Selected Mathematical Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663

BOOK REVIEWS

Guoliang Yu (Reviewer), Basic noncommutative geometry, 2nd edition, byMasoud Khalkhali . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675

Laurent Bartholdi (Reviewer), Combinatorial algebra: syntax andsemantics, by Mark V. Sapir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681

Stamp picturing C. F. Gauss issued by Deutsche Bundespost in 1955.

INDEX TO VOLUME 54 (2017)

bulletin articles

Bauer, Andrej. Five stages of accepting constructive mathematics, 481

Colmez, Pierre. Tate’s work and the Serre–Tate correspondence, 559Curto, Carina. What can topology tell us about the neural code?, 63

De Lellis, Camillo, and Laszlo Szekelyhidi Jr. High dimensionality and h-principle in PDE, 247

Friedlander, Susan. Introduction to the Nash issue, 171. Introduction to the Tate issue, 541

Gowers, W. T. Generalizations of Fourier analysis, and how to apply them, 1. Probabilistic combinatorics and the recent work of Peter Keevash, 107

Gromov, Misha. Geometric, algebraic, and analytic descendants of Nash isometric embedding

theorems, 173

Hauser, Herwig. The classical Artin approximation theorems, 595Klainerman, Sergiu. On Nash’s unique contribution to analysis in just three of his papers, 283

Kollar, Janos. Nash’s work in algebraic geometry, 307Laurencot, Philippe, and Christoph Walker. Some singular equations modeling MEMS, 437

Levine, Lionel, and Yuval Peres. Laplacian growth, sandpiles, and scaling limits, 355

Merkurjev, Alexander S. Essential dimension, 635Milne, J. S. The work of John Tate, 544

. Review of the Collected Works of John Tate, 551

Pelayo, Alvaro. Hamiltonian and symplectic symmetries: An introduction, 383

Peres, Yuval. See Levine, Lionel

Silverman, Joseph H. Rational points on, and the arithmetic of, elliptic curves: A tale of twobooks (and an article), 591

Spielman, Daniel A. Graphs, vectors, and matrices, 45

Szekelyhidi, Laszlo, Jr. See De Lellis, CamilloTate, John. Number theory in the 20th century: Part 1, 547

Totaro, Burt. Recent progress on the Tate conjecture, 575

Walker, Christoph. See Laurencot, PhilippeWilkinson, Amie. What are Lyapunov exponents, and why are they interesting?, 79

mathematical perspectives

Alexanderson, Gerald L. About the cover: Newton’s Principia, 117. About the cover: Leonhard Euler, teacher and mentor, 499

book reviews

Aizenman, Michael, and Simone Warzel. Random operators: disorder effects on quantum spectra

and dynamics, reviewed by Gunter Stolz, 347Artstein-Avidan, Shiri, Apostolos Giannopoulos, and Vitali D. Milman. Asymptotic geometric

analysis, Part I, reviewed by Gideon Schechtman, 341

Bellettini, Giovanni. Lecture notes on mean curvature flow: barriers and singular perturbations,reviewed by William P. Minicozzi II, 529

Foucart, S., and H. Rauhut. A mathematical introduction to compressive sensing, reviewed by

Joel A. Tropp, 151Giannopoulos, Apostolos. See Artstein-Avidan, Shiri

Gu, Xianfeng David. See Zeng, Wei

Kaliuzhnyi-Verbovetskyi, Dmitry S., and Victor Vinnikov. Foundation of free noncommutativefunction theory, reviewed by Vladimir Retakh, 533

Khalkhali, Masoud. Basic noncommutative geometry, 2nd edition, reviewed by Guoliang Yu,

675Milman, Vitali D. See Artstein-Avidan, Shiri

Polterovich, Leonid, and Daniel Rosen. Function theory on symplectic manifolds, reviewed byYakov Eliashberg, 135

Rauhut, H. See Foucart, S.

Rosen, Daniel. See Polterovich, LeonidSapir, Mark V. Combinatorial algebra: syntax and semantics, reviewed by Laurent Bartholdi,

681

INDEX TO VOLUME 54 (2017)

Schilling, Rene L., Zoran Vondracek, and Wojbor A. Woyczynski (Editors). William Feller,

Selected papers I, reviewed by Anthony G. Pakes, 537

Schilling, Rene L., Zoran Vondracek, and Wojbor A. Woyczynski (Editors). William Feller,Selected papers II, reviewed by Anthony G. Pakes, 537

Stillwell, John. Elements of mathematics: from Euclid to Godel, reviewed by Victor J. Katz,

521van Suijlekom, Walter D. Noncommutative geometry and particle physics, reviewed by Matilde

Marcolli, 167

Touzi, N. Optimal stochastic control, stochastic target problems, and backward SDE, reviewedby Jaime San Martın, 333

Vinnikov, Victor. See Kaliuzhnyi-Verbovetskyi, Dmitry S.

Vondracek, Zoran. See Schilling, Rene L.. See Schilling, Rene L.

Warzel, Simone. See Aizenman, MichaelWoyczynski, Wojbor A. See Schilling, Rene L.

. See Schilling, Rene L.

Zeng, Wei, and Xianfeng David Gu. Ricci flow for shape analysis and surface registration: the-ories, algorithms and applications, reviewed by Bennett Chow, David Glickenstein, and

Feng Luo, 141

BULLETIN( N E W S E R I E S ) OF THE

A M E R I C A N M A T H E M A T I C A L S O C I E T Y

PROVIDENCE, RHODE ISLAND USA

ISSN 0273-0979

VOLUME 54 2017

Available electronically at www.ams.org/bull/

EDITORSSusan Friedlander, Chief EditorPeter Kuchment, Book Reviews

ASSOCIATE EDITORS

Emmanuel CandesDavid CoxRichard T. DurrettMark EmbreeDaniel S. FreedEdward Frenkel Irene M. GambaMark GoreskyAndrew J. GranvilleRobert M. GuralnickCraig HunekeLisa Jeffrey Bryna Kra

Steven G. KrantzBarry C. Mazur William P. Minicozzi IIKen OnoAndrew A. RanickiPhilip E. ProtterIsrael Michael Singer Christoph M. Thiele Burt TotaroYuri TschinkelMichael Wolf Maciej Zworski

CONSULTANTS TO THE EDITORSGerald L. AlexandersonEdward Dunne

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY

CONTENTS

Vol. 54, No. 1 January 2017

Articles

W. T. Gowers, Generalizations of Fourier analysis, and how to apply them 1

Daniel A. Spielman, Graphs, vectors, and matrices . . . . . . . . . . . . . . . . . . . . . . 45

Carina Curto, What can topology tell us about the neural code? . . . . . . . . . 63

Amie Wilkinson, What are Lyapunov exponents, and why are theyinteresting? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

W. T. Gowers, Probabilistic combinatorics and the recent work of PeterKeevash . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

Mathematical Perspectives

Gerald L. Alexanderson, About the cover: Newton’s Principia . . . . . . . . . 117

Selected Mathematical Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

Book Reviews

Yakov Eliashberg (Reviewer), Function theory on symplectic manifolds, byLeonid Polterovich and Daniel Rosen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

Bennett Chow, David Glickenstein, and Feng Luo (Reviewers), Ricciflow for shape analysis and surface registration: theories, algorithms andapplications, by Wei Zeng and Xianfeng David Gu . . . . . . . . . . . . . . . . . . . 141

Joel A. Tropp (Reviewer), A mathematical introduction to compressivesensing, by S. Foucart and H. Rauhut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

Matilde Marcolli (Reviewer), Noncommutative geometry and particlephysics, by Walter D. van Suijlekom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

Vol. 54, No. 2 April 2017

Articles

Susan Friedlander, Introduction to the Nash issue . . . . . . . . . . . . . . . . . . . . . . . 171

Misha Gromov, Geometric, algebraic, and analytic descendants of Nashisometric embedding theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

Camillo De Lellis and Laszlo Szekelyhidi Jr., High dimensionality andh-principle in PDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

Sergiu Klainerman, On Nash’s unique contribution to analysis in just threeof his papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283

Janos Kollar, Nash’s work in algebraic geometry . . . . . . . . . . . . . . . . . . . . . . . . . 307

Mathematical Perspectives

Selected Mathematical Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

Book Reviews

Jaime San Martın (Reviewer), Optimal stochastic control, stochastic targetproblems, and backward SDE, by N. Touzi . . . . . . . . . . . . . . . . . . . . . . . . . . . 333

Gideon Schechtman (Reviewer), Asymptotic geometric analysis, Part I, byShiri Artstein-Avidan, Apostolos Giannopoulos, and Vitali D. Milman 341

Gunter Stolz (Reviewer), Random operators: disorder effects on quantumspectra and dynamics, by Michael Aizenman and Simone Warzel . . . . . 347

Vol. 54, No. 3 July 2017

Articles

Lionel Levine and Yuval Peres, Laplacian growth, sandpiles, and scalinglimits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

Alvaro Pelayo, Hamiltonian and symplectic symmetries: An introduction 383

Philippe Laurencot and Christoph Walker, Some singular equationsmodeling MEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 437

Andrej Bauer, Five stages of accepting constructive mathematics . . . . . . . . 481

Mathematical Perspectives

Gerald L. Alexanderson, About the cover: Leonhard Euler, teacher andmentor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499

Selected Mathematical Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 505

Book Reviews

Victor J. Katz (Reviewer), Elements of mathematics: from Euclid to Godel,by John Stillwell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521

William P. Minicozzi II (Reviewer), Lecture notes on mean curvature flow:barriers and singular perturbations, by Giovanni Bellettini . . . . . . . . . . . 529

Vladimir Retakh (Reviewer), Foundation of free noncommutative functiontheory, by Dmitry S. Kaliuzhnyi-Verbovetskyi and Victor Vinnikov . . 533

Anthony G. Pakes (Reviewer), William Feller, Selected papers I, editedby Rene L. Schilling, Zoran Vondracek, and Wojbor A. Woyczynski;William Feller, Selected papers II, edited by Rene L. Schilling, ZoranVondracek, and Wojbor A. Woyczynski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537

Vol. 54, No. 4 October 2017

Articles

Susan Friedlander, Introduction to the Tate issue . . . . . . . . . . . . . . . . . . . . . . . 541

J. S. Milne, The work of John Tate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544

John Tate, Number theory in the 20th century: Part 1 . . . . . . . . . . . . . . . . . . . 547

J. S. Milne, Review of the Collected Works of John Tate . . . . . . . . . . . . . . . . . 551

Pierre Colmez, Tate’s work and the Serre–Tate correspondence . . . . . . . . . . 559

Burt Totaro, Recent progress on the Tate conjecture . . . . . . . . . . . . . . . . . . . . . 575

Joseph H. Silverman, Rational points on, and the arithmetic of, ellipticcurves: A tale of two books (and an article) . . . . . . . . . . . . . . . . . . . . . . . . . . 591

Herwig Hauser, The classical Artin approximation theorems . . . . . . . . . . . . . 595

Alexander S. Merkurjev, Essential dimension . . . . . . . . . . . . . . . . . . . . . . . . . . 635

Mathematical Perspectives

Selected Mathematical Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663

Book Reviews

Guoliang Yu (Reviewer), Basic noncommutative geometry, 2nd edition, byMasoud Khalkhali . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675

Laurent Bartholdi (Reviewer), Combinatorial algebra: syntax andsemantics, by Mark V. Sapir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681

Editorial Board for Articles

Emmanuel CandesRichard T. DurrettDaniel S. FreedEdward FrenkelSusan Friedlander, ChairIrene M. GambaMark GoreskyAndrew J. GranvilleRobert M. Guralnick

Bryna R. KraBarry C. MazurWilliam P. Minicozzi IIAndrew RanickiChristoph M. ThieleBurt TotaroYuri TschinkelMichael WolfMaciej Zworski

Editorial Board for Book Reviews

David CoxMark EmbreeCraig L. HunekeLisa JeffreySteven G. Krantz

Peter Kuchment, ChairKen OnoPhilip E. ProtterIsrael Michael Sigal

Consultants to the Editors

Gerald L. AlexandersonEdward Dunne

Chief Editor: Susan Friedlander

Editorial Information

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BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY

CONTENTS

Vol. 54, No. 4 October 2017

ARTICLES

Susan Friedlander, Introduction to the Tate issue . . . . . . . . . . . . . . . . . . . . . . . 541

J. S. Milne, The work of John Tate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544

John Tate, Number theory in the 20th century: Part 1 . . . . . . . . . . . . . . . . . . . 547

J. S. Milne, Review of the Collected Works of John Tate . . . . . . . . . . . . . . . . . 551

Pierre Colmez, Tate’s work and the Serre–Tate correspondence . . . . . . . . . . 559

Burt Totaro, Recent progress on the Tate conjecture . . . . . . . . . . . . . . . . . . . . 575

Joseph H. Silverman, Rational points on, and the arithmetic of, elliptic

curves: A tale of two books (and an article) . . . . . . . . . . . . . . . . . . . . . . . . . . 591

Herwig Hauser, The classical Artin approximation theorems . . . . . . . . . . . . 595

Alexander S. Merkurjev, Essential dimension . . . . . . . . . . . . . . . . . . . . . . . . . . 635

MATHEMATICAL PERSPECTIVES

Selected Mathematical Reviews . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663

BOOK REVIEWS

Guoliang Yu (Reviewer), Basic noncommutative geometry, 2nd edition, by

Masoud Khalkhali . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675

Laurent Bartholdi (Reviewer), Combinatorial algebra: syntax and

semantics, by Mark V. Sapir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681