From Topology to Computation: Proceedings of the Smalefest

1. Front Matter

   Pages i-xxix

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2. Autobiographical Material

   1. Front Matter

      Pages 1-1

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   2. Some Autobiographical Notes

      • Steve Smale

      Pages 3-21

   3. On How I Got Started In Dynamical Systems, 1959–1962

      • Steve Smale

      Pages 22-26

   4. The Story of the Higher Dimensional Poincaré Conjecture (What Actually Happened on the Beaches of Rio)

      • Steve Smale

      Pages 27-40

   5. On the Steps of Moscow University

      • Steve Smale

      Pages 41-52

   6. Professional Biography, Bibliography, and Graduate Students

      • Steve Smale

      Pages 53-63

3. Informal Talks

   1. Front Matter

      Pages 65-65

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   2. Luncheon Talk and Nomination for Stephen Smale

      • R. Bott

      Pages 67-72

   3. Some Recollections of the Early Work of Steve Smale

      • M. M. Peixoto

      Pages 73-75

   4. Luncheon Talk

      • R. Thom

      Pages 76-78

   5. Banquet Address at the Smalefest

      • E. C. Zeeman

      Pages 79-80

4. Differential Topology

   1. Front Matter

      Pages 81-81

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   2. The Work of Stephen Smale in Differential Topology

      • Morris W. Hirsch

      Pages 83-106

   3. Discussions

      1. Discussion

         • J. Stallings, A. Haefliger

         Pages 107-113

      2. Note on the History of Immersion Theory

         • David Spring

         Pages 114-116

   4. Contributed Paper

      1. The Smale—Hirsch Principle in Catastrophe Theory

         • V. A. Vassil’ev

         Pages 117-128

5. Economics

   1. Front Matter

      Pages 129-129

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   2. Stephen Smale and the Economic Theory of General Equilibrium

      • Gerard Debreu

      Pages 131-146

   3. Discussions

      1. Topology and Economics: The Contribution of Stephen Smale

         • Graciela Chichilnisky

         Pages 147-161

An extraordinary mathematical conference was held 5-9 August 1990 at the University of California at Berkeley: From Topology to Computation: Unity and Diversity in the Mathematical Sciences An International Research Conference in Honor of Stephen Smale's 60th Birthday The topics of the conference were some of the fields in which Smale has worked: • Differential Topology • Mathematical Economics • Dynamical Systems • Theory of Computation • Nonlinear Functional Analysis • Physical and Biological Applications This book comprises the proceedings of that conference. The goal of the conference was to gather in a single meeting mathemati­ cians working in the many fields to which Smale has made lasting con­ tributions. The theme "Unity and Diversity" is enlarged upon in the section entitled "Research Themes and Conference Schedule." The organizers hoped that illuminating connections between seemingly separate mathematical sub­ jects would emerge from the conference. Since such connections are not easily made in formal mathematical papers, the conference included discussions after each of the historical reviews of Smale's work in different fields. In addition, there was a final panel discussion at the end of the conference.

• Approximation
• Convexity
• Eigenvalue
• Minimal surface
• algorithms
• calculus
• catastrophe theory
• differential equation
• functional analysis
• manifold
• mathematical economics
• minimum

• Department of Mathematics, University of California, Berkeley, USA

  Morris W. Hirsch, Jerrold E. Marsden

• IBM Research, T.J. Watson Research Center, Yorktown Heights, USA

  Michael Shub

Policies and ethics