Proceedings of the International Congress of Mathematicians 1998

Ulf Rehmann; Gerd Fischer

doi:10.4171/dms/1-2

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