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DOCUMENTA MATHEMATICA Extra Volume
PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS Berlin 1998, August 18 - 27 Volume I : Plenary Lectures and Ceremonies (662 pages) • • • • • •
Ceremonies (p. 11-98) The Work of the Fields Medalists and the Rolf Nevanlinna Prize Winner (p. 99-142) Invited One-Hour Plenary Lectures (p. 143-606) Lectures by the Fields Medalists and the Rolf Nevanlinna Prize Winner (p. 607-632) Appendix (p. 633-658) (Three Invited Forty-Five Minute Lectures not included in Volumes II and III) Author Index for Volumes I, II, III: (p. 659-662)
Volume II : Invited Lectures (881 pages) Invited Forty-Five Minute Lectures at the Section Meetings, Sections 1 - 9 • • • • • • • • • •
1. Logic (p. 11-54), see also Appendix Vol. I 2. Algebra (p. 55-140) 3. Number Theory and Arithmetic Algebraic Geometry (p. 141-228) 4. Algebraic Geometry (p. 229-288) 5. Differential Geometry and Global Analysis (p. 289-422) 6. Topology (p. 423-506) 7. Lie Groups and Lie Algebras (p. 507-616) 8. Analysis (p. 617-764) 9. Ordinary Differential Equations and Dynamical Systems (p. 765-878) Author Index for Volumes II, III: (p. 879-881)
Volume III : Invited Lectures (825 pages) Invited Forty-Five Minute Lectures at the Section Meetings, Sections 10 - 19 • • • • • • • • • • •
10. Partial Differential Equations (p. 11-98), see also Appendix Vol. I 11. Mathematical Physics (p. 99-204) 12. Probability and Statistics (p. 205-332)) 13. Combinatorics (p. 333-422) 14. Mathematical Aspects of Computer Science (p. 421-480) 15. Numerical Analysis and Scientific Computing (p. 481-544 ) 16. Applications, see also Appendix Vol. I (p. 545-644) 17. Control Theory and Optimization (p. 645-719) 18. Teaching and Popularization of Mathematics (p. 719-788) 19. History of Mathematics (p. 789-822) Author Index for Volumes II, III: (p. 823-825)
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ICM 1998 Contents of Volumes I, II, and III Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Past Congresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Past Fields Medalists and Rolf Nevanlinna Prize Winners . . . . . . . . . . . . ¨ tschel: Organization of the Congress . . . . . . . . . . . . . . . . . Martin Gro The Committees of the Congress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Donors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Opening Ceremony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Yuri I. Manin: Presentation of the Fields Medals and a Special Tribute . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . David Mumford: Presentation of the Rolf Nevanlinna Prize . . . . . . . . Fax to the Federal President and to the Governing Mayor . . . . . . . . . . . . Closing Ceremony . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Participants by Country . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
I I I I I I I
11 12 13 15 19 21 23
I I I I I I
45 49 50 53 61 96
I I I I I
99 109 119 127 133
I
143
I
163
I
187
I
205
I
235
I I
255 281
I I I
303 319 339
The Work of the Fields Medalists and of the Rolf Nevanlinna Prize Winner Peter Goddard: The Work of Richard Ewen Borcherds . . . .