Proceedings of the International Congress of Mathematicians 1998

The Proceedings of the International Congress of Mathematicians 1998, held in Berlin, are published – electronically and in print – in three volumes. Volume I contains information on the organization of the Congress including the list of participants, reports on the opening and closing ceremonies, the Laudationes on the Fields Medalists and the Nevanlinna Prize Winner, and the Plenary Lectures. Volumes II and III contain the Invited Lectures.

pp. 11–21
Generic large cardinals: New axioms for mathematics?
Matthew Foreman
DOI 10.4171/DMS/1-2/1
pp. 23–32
When is an equivalance relation classifiable
Greg Hjorth
DOI 10.4171/DMS/1-2/2
pp. 33–42
Meager forking and $m$ -independence
Ludomir Newelski
DOI 10.4171/DMS/1-2/3
pp. 43–52
Basis problems in combinatorial set theory
Stevo Todorcevic
DOI 10.4171/DMS/1-2/4
pp. 55–65
Geometry of infinitesimal group schemes
Eric M. Friedlander
DOI 10.4171/DMS/1-2/5
pp. 67–75
On the Burnside problem for groups of even exponent
Sergei V. Ivanov
DOI 10.4171/DMS/1-2/6
pp. 77–86
Simple groups in computational group theory
William M. Kantor
DOI 10.4171/DMS/1-2/7
pp. 87–96
Spetses
Gunter Malle
DOI 10.4171/DMS/1-2/8
pp. 97–107
Birational automorphisms of higher-dimensional algebraic varieties
Aleksandr V. Pukhlikov
DOI 10.4171/DMS/1-2/9
pp. 109–120
Tilting theory and quasitilted algebras
Idun Reiten
DOI 10.4171/DMS/1-2/10
pp. 121–128
The Abelian defect group conjecture
Jeremy Rickard
DOI 10.4171/DMS/1-2/11
pp. 129–137
Simple groups, permutation groups, and probability
Aner Shalev
DOI 10.4171/DMS/1-2/12
pp. 141–151
$p$ -adic analytic spaces
Vladimir G. Berkovich
DOI 10.4171/DMS/1-2/13
pp. 153–162
$p$ -adic representations of a local field
Pierre Colmez
DOI 10.4171/DMS/1-2/14
pp. 163–172
Bounds for arithmetic multiplicities
W. Duke
DOI 10.4171/DMS/1-2/15
pp. 173–182
Some results on algebraic independence
François Gramain
DOI 10.4171/DMS/1-2/16
pp. 183–186
Rational points and Dirichlet series
Loïc Merel
DOI 10.4171/DMS/1-2/17
pp. 187–196
The intrinsic Hodge theory of $p$ -adic hyperbolic curves.
Shinichi Mochizuki
DOI 10.4171/DMS/1-2/18
pp. 197–205
The subspace theorem and applications
Hans Peter Schlickewei
DOI 10.4171/DMS/1-2/19
pp. 207–216
$p$ -adic Hodge theory in the semi-stable reduction case
Takeshi Tsuji
DOI 10.4171/DMS/1-2/20
pp. 217–225
Small points and Arakelov theory
Shou-Wu Zhang
DOI 10.4171/DMS/1-2/21
pp. 229–238
String theory and duality
Paul S. Aspinwall
DOI 10.4171/DMS/1-2/22
pp. 239–248
Mirror symmetry and toric geometry
Victor V. Batyrev
DOI 10.4171/DMS/1-2/23
pp. 249–257
Cohomology of moduli spaces of stable curves
Maurizio Cornalba
DOI 10.4171/DMS/1-2/24
pp. 259–265
Barsotti-Tate groups and crystals
A.J. de Jong
DOI 10.4171/DMS/1-2/25
pp. 267–276
Higher Abel-Jacobi maps
Mark L. Green
DOI 10.4171/DMS/1-2/26
pp. 277–286
Operads and algebraic geometry
M. Kapranov
DOI 10.4171/DMS/1-2/27
pp. 289–298
Hard balls gas and Alexandrov spaces of curvature bounded above
Dmitri Burago
DOI 10.4171/DMS/1-2/28
pp. 299–308
Spaces with Ricci curvature bounds
Tobias H. Colding
DOI 10.4171/DMS/1-2/29
pp. 309–314
Lefschetz fibrations in symplectic geometry
S.K. Donaldson
DOI 10.4171/DMS/1-2/30
pp. 315–326
Geometry and analytic theory of Frobenius manifolds
Boris Dubrovin
DOI 10.4171/DMS/1-2/31
pp. 327–338
Invariants in contact topology
Yakov Eliashberg
DOI 10.4171/DMS/1-2/32
pp. 339–348
Curvature-decreasing maps are volume-decreasing. On joint work with G. Besson and G. Courtois
S. Gallot
DOI 10.4171/DMS/1-2/33
pp. 349–360
Evolution of hypersurfaces by their curvature in Riemannian manifolds
Gerhard Huisken
DOI 10.4171/DMS/1-2/34
pp. 361–370
Compact manifolds with exceptional holonomy
Dominic Joyce
DOI 10.4171/DMS/1-2/35
pp. 371–380
Large group actions on manifolds
François Labourie
DOI 10.4171/DMS/1-2/36
pp. 381–388
Curvature contents of geometric spaces
Joachim Lohkamp
DOI 10.4171/DMS/1-2/37
pp. 389–400
Quaternionic analysis on Riemann surfaces and differential geometry
Franz PeditUlrich Pinkall
DOI 10.4171/DMS/1-2/38
pp. 401–410
Geometry on the group of Hamiltonian diffeomorphisms
Leonid Polterovich
DOI 10.4171/DMS/1-2/39
pp. 411–420
Quantum cohomology and its application
Yongbin Ruan
DOI 10.4171/DMS/1-2/40
pp. 423–432
Dimension theory and large Riemannian manifolds
A.N. Dranishnikov
DOI 10.4171/DMS/1-2/41
pp. 433–442
Lie groups and $p$ -compact groups
W.G. Dwyer
DOI 10.4171/DMS/1-2/42
pp. 443–452
Constructions of smooth 4-manifolds
Ronald FintushelRonald J. Stern
DOI 10.4171/DMS/1-2/43
pp. 453–464
Topological views on computational complexity
Michael H. Freedman
DOI 10.4171/DMS/1-2/44
pp. 465–472
Toward a global understanding of $π_{*} (S^{n})$
Mark Mahowald
DOI 10.4171/DMS/1-2/45
pp. 473–482
A filtration of the set of integral homological 3-spheres
Tomotada Ohtsuki
DOI 10.4171/DMS/1-2/46
pp. 483–492
Vector bundles over classifying spaces
Bob Oliver
DOI 10.4171/DMS/1-2/47
pp. 493–504
The geometry of the Seiberg-Witten invariants
DOI 10.4171/DMS/1-2/48
pp. 507–517
Towards a stable trace formula
James Arthur
DOI 10.4171/DMS/1-2/49
pp. 519–525
Analytic structures on representation spaces of reductive groups
Joseph Bernstein
DOI 10.4171/DMS/1-2/50
pp. 527–537
From double Hecke algebra to analysis
Ivan Cherednik
DOI 10.4171/DMS/1-2/51
pp. 539–552
Counting problems and semisimple groups
Alex Eskin
DOI 10.4171/DMS/1-2/52
pp. 553–562
Harmonic analysis on semisimple $p$ -adic Lie algebras
Robert E. Kottwitz
DOI 10.4171/DMS/1-2/53
pp. 563–570
Drinfeld shtukas and applications
L. Lafforgue
DOI 10.4171/DMS/1-2/54
pp. 571–582
Products of trees, lattices and simple groups
Shahar Mozes
DOI 10.4171/DMS/1-2/55
pp. 583–593
Characters of irreducible representations of simple Lie superalgebras
Vera Serganova
DOI 10.4171/DMS/1-2/56
pp. 595–604
Topological methods in representation theory
Kari Vilonen
DOI 10.4171/DMS/1-2/57
pp. 605–614
Representation theory of affine superalgebras at the critical level
Minoru Wakimoto
DOI 10.4171/DMS/1-2/58
pp. 617–626
Analytic aspects of quasiconformality
Kari Astala
DOI 10.4171/DMS/1-2/59
pp. 627–636
Singularity and regularity -- local and global
Michael Christ
DOI 10.4171/DMS/1-2/60
pp. 637–646
The Baum-Connes conjecture
Nigel Higson
DOI 10.4171/DMS/1-2/61
pp. 647–656
On the bilinear Hilbert transform
Michael T. Lacey
DOI 10.4171/DMS/1-2/62
pp. 657–664
Rectifiability, analytic capacity, and singular integrals
Pertti Mattila
DOI 10.4171/DMS/1-2/63
pp. 665–677
Randomness and pattern in convex geometric analysis
Vitali Milman
DOI 10.4171/DMS/1-2/64
pp. 679–689
Functional calculus of Lie groups and wave propagation
Detlef Müller
DOI 10.4171/DMS/1-2/65
pp. 691–702
Unexpected solutions of first and second order partial differential equations
Stefan MüllerVladimir Šverák
DOI 10.4171/DMS/1-2/66
pp. 703–712
Reflection principle in higher dimensions
Klas DiederichSergey Pinchuk
DOI 10.4171/DMS/1-2/67
pp. 713–722
Developments from nonharmonic Fourier series
Kristian Seip
DOI 10.4171/DMS/1-2/68
pp. 723–730
Wave equations with low regularity coefficients
Hart F. Smith
DOI 10.4171/DMS/1-2/69
pp. 731–742
From finite- to infinite-dimensional phenomena in geometric functional analysis on local and asymptotic levels
Nicole Tomczak-Jaegermann
DOI 10.4171/DMS/1-2/70
pp. 743–753
Discrete analogues of singular and maximal Radon transforms
Stephen Wainger
DOI 10.4171/DMS/1-2/71
pp. 755–761
Maximal averages and packing of one dimensional sets
Thomas Wolff
DOI 10.4171/DMS/1-2/72
pp. 765–778
Rigidity and renormalization in one dimensional dynamical systems
W. de Melo
DOI 10.4171/DMS/1-2/73
pp. 779–787
Reducibility and point spectrum for linear quasi-periodic skew-products
L.H. Eliasson
DOI 10.4171/DMS/1-2/74
pp. 789–796
Hyperbolicity, stability, and the criterion of homoclinic points
Shuhei Hayashi
DOI 10.4171/DMS/1-2/75
pp. 797–808
Some open problems in dynamical systems
Michael Herman
DOI 10.4171/DMS/1-2/76
pp. 809–818
Random dynamics and its applications
Yuri Kifer
DOI 10.4171/DMS/1-2/77
pp. 819–829
Elements of a qualitative theory of Hamiltonian PDEs
Sergei B. Kuksin
DOI 10.4171/DMS/1-2/78
pp. 831–840
Counterexamples to the Seifert conjecture
Krystyna Kuperberg
DOI 10.4171/DMS/1-2/79
pp. 841–855
Rigidity and inflexibility in conformal dynamics
Curtis T. McMullen
DOI 10.4171/DMS/1-2/80
pp. 857–866
Induced hyperbolicity for one-dimensional maps
Grzegorz Świątek
DOI 10.4171/DMS/1-2/81
pp. 867–877
Arnold diffusion: a variational construction
Zhihong Xia
DOI 10.4171/DMS/1-2/82