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Fields Medallists' Lectures

Sir Michael Atiyah, Daniel Iagolnitzer, and Chitat Chong, editors
World Scientific
Publication Date: 
Number of Pages: 
World Scientific Series on 21rst Century Mathematics, Volume 1
BLL Rating: 

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Fernando Q. Gouvêa
, on

See our review of the second edition. The main goal of this edition is to include contributions by the Fields Medalists up to 2010 (not, therefore the latest ones). Added to the collection are lectures by John Milnor, Enrico Bombieri, Gerd Faltings, Andrei Okounkov, Terence Tao, Cédric Villani, Elon Lindenstrauss, Ngô Bâu Châu, and Stanislav Smirnov. Also added are survey lectures on the work of Michael Atiyah, Alexander Grothendieck, Stephen Smale, and Jean-Christophe Yoccoz; these are newly translated from French, but presumably were the original ICM lectures about their work.

As we noted in our previous review, not all Fields Medalists are represented. Most readers will find the survey articles on each mathematician’s work the most accessible and interesting part of the book. (The so-called “biographical notices” are typically very brief, though there are some welcome exceptions to that rule.) The “lectures” themselves can be quite technical.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME.

  • 1936 L V Ahlfors:
    • Quasiconformal Mappings, Teichmüller Spaces, and Kleinian Groups
  • 1950 L Schwartz:
    • The Work of L Schwartz by H Bohr
    • Calcul Infinitesimal Stochastique
  • 1954 K Kodaira:
    • Obituary: Kunihiko Kodaira
    • On Kähler Varieties of Rrestricted Type
  • 1958 K F Roth:
    • The Work of K F Roth by H Davenport
    • Rational Approximations to Algebraic Numbers
  • R Thom:
    • The Work of R Thom by H Hopf
  • 1962 L Hörmanjder:
    • Hörmanjder's Work on Linear Differential Operators by L Gårding
    • Looking Forward from ICM 1962
  • J W Milnor:
    • The Work of John W Milnor by H Whitney
    • Topological Manifolds and Smooth Manifolds
  • 1966 M F Atiyah:
    • The Work of Michael F Atiyah by H Cartan
    • The Index of Elliptic Operators
  • Paul J Cohen:
    • The Continuum Problem by A Church
  • Alexander Grothendieck:
    • The Works of Alexander Grothendieck by Jean Dieudonné
  • S Smale:
    • On the Works of Stephen Smale by R Thom
    • A Survey of Some Recent Developments in Differential Topology
  • 1970 A Baker:
    • The Work of Alan Baker by P Turán
    • Effective Methods in the Theory of Numbers
    • Effective Methods in Diophantine Problems
    • Effective Methods in Diophantine Problems. II
    • Effective Methods in the Theory of Numbers/Diophantine Problems
  • S Novikov:
    • The Work of Serge Novikov by M F Atiyah
    • Rôle of Integrable Models in the Development of Mathematics
  • 1974 E Bombieri:
    • The Work of Enrico Bombieri by K Chandrasekharan
    • Variational Problems and Elliptic Equations
  • D Mumford:
    • The Work of David Mumford by J Tate
    • Pattern Theory: A Unifying Perspective
  • 1978 G A Margulis:
    • The Work of Gregory Aleksandrovitch Margulis by J Tits
    • Oppenheim Conjecture
  • 1982 A Connes:
    • The Work of Alain Connes by H Araki
    • Brisure de Symétrie Spontanée et Géométrie du Point de vue Spectral
    • W P Thurston: The Work of W Thurston by C T C Wall
  • W P Thurston:
    • The Work of W Thurston by C T C Wall
  • 1986 S K Donaldson:
    • The Work of Simon Donaldson by M F Atiyah
    • Remarks on Gauge Theory, Complex Geometry and 4-Manifold Topology
  • G Faltings:
    • On Some of the Mathematical Contributions of Gerd Faltings by B Mazur
    • Neuere Entwicklungen in der Arithmetischen Algebraischen Geometrie
  • M H Freedman:
    • The Work of M H Freedman by J Milnor
    • Betti Number Estimates for Nilpotent Groups
  • 1990 V F R Jones:
    • The Work of Vaughan F R Jones by J S Birman
    • A Polynomial Invariant for Knots via Von Neumann Algebras
    • Index for Subfactors
  • S Mori:
    • The Work of Shigefumi Mori by H Hironaka
    • Birational Classification of Algebraic Threefolds
  • E Witten:
    • The Work of E Witten by L D Faddeev
    • The Work of Edward Witten by M F Atiyah
    • Geometry and Quantum Field Theory
  • 1994 J Bourgain:
    • The Work of Jean Bourgain by L Caffarelli
    • Hamiltonian Methods in Nonlinear Evolution Equations
  • P L Lions::
    • The Work of Pierre-Louis Lions by S R S Varadhan
    • On Some Recent Methods for Nonlinear Partial Differential Equations
  • J C Yoccoz:
    • Presentation de Jean-Christophe Yoccoz by A Douady
    • Recent Developments in Dynamics
  • E I Zelmanov:
    • The Work of Efim Zelmanov by W Feit
    • On the Restricted Burnside Problem
  • 1998 R E Borcherds:
    • The Work of Richard Ewen Borcherds by P Goddard
    • What is Moonshine?
  • W T Gowers:
    • The Work of William Timothy Gowers by B Bollobás
    • A New Proof of Szemerédi's Theorem for Arithmetic Progressions of Length Four
  • M Kontsevich:
    • The Work of Maxim Kontsevich by C H Taubes
    • Formal (Non)-Commutative Symplectic Geometry
    • Comments on "Formal (Non)-Commutative Symplectic Geometry"
  • C T McMullen:
    • The Work of Curtis T McMullen by J Milnor
    • Rigidity and Inflexibility in Conformal Dynamics
  • 2002 L Lafforgue:
    • The Work of Laurent Lafforgue by G Laumon
  • V Voevodsky:
    • The Work of Vladimir Voevodsky by C Soulé
    • Open Problems in the Motive Stable Homotopy Theory, I
  • 2006 A Okounkov:
    • The Work of Andrei Okounkov by G Felder
  • Terence Tao:
    • The Work of Terence Tao by C Fefferman
    • The Dichotomy between Structure and Randomness, Arithmetic Progressions, and the Primes
  • 2010 Ngô Bao Châu:
    • The Work of Ngô Bao Châu by J Arthur
    • Endoscopy Theory of Automorphic Forms
  • E Lindenstrauss:
    • The Work of Elon Lindenstrauss by H Furstenberg
    • Equidistribution in Homogeneous Spaces and Number Theory
  • S Smirnov:
    • The Work of Stanislav Smirnov by H Kesten
    • Discrete Complex Analysis and Probability
  • C Villani:
    • The Work of Cédric Villani by H-T Yau, Landau Damping