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Structure of the Program/ICM98 Sections Below is a message from Phillip A. Griffiths, Chairman of the ICM-98 Program Committee describing the current plans concerning the structure of the scientific program. Dear Colleague: The Program Committee for ICM-98 had a very productive first meeting at the Institute for Advanced Study in Princeton, New Jersey this past December. Committee members came to the meeting with suggestions from their colleagues for sections, panel members, and plenary speakers, and these formed the basis for our preliminary recommendations. Since our meeting, we have continued to consult among ourselves and with other colleagues, and we have refined our lists based on input from many sources. Our goal has been to organize the sections and to select panel members so that they reflect current research in mathematics. The results of our discussions are perhaps best presented by simply enclosing herewith our list of sections, which includes the number of talks (in parentheses) to be assigned to each. We look forward to seeing you in Berlin in 1998. Yours truly, Phillip A. Griffiths Chairman ICM-98 Program Committee ENCLOSURE ICM-98 Section Descriptions (9/24/96) 1. Logic Model theory. Set theory and general topology. Recursion. Logics. Proof theory. Applications. Connections with sections 2, 3, 13, 14 2. Algebra Finite and infinite groups. Rings and algebras. Representations of finite dimensional algebras. Algebraic K-theory. Category theory and homological algebra. Computational algebra. Geometric methods in group theory. Connections with sections 1, 3, 4, 6, 7, 13, 14 3. Number Theory and Arithmetic Algebraic Geometry Algebraic and analytic number theory. Zeta and L-functions. Modular functions (except general automorphic theory). Arithmetic on algebraic varieties. Diophantine equations, Diophantine approximation. Transcendental number theory, geometry of numbers. p-adic analysis. Computational number theory. Arakelov theory. Galois representations. Connections with sections 1, 2, 4, 7, 13, 14 4. Algebraic Geometry (joint piece with #11) Algebraic varieties, their cycles, cohomologies and motives. Singularities and classification. Includes moduli spaces. Low dimensional varieties. Abelian varieties. Vector bundles. Real algebraic and analytic sets. Connections with sections 2, 3, 5, 6, 7, 13, 14 5. Differential Geometry and Global Analysis Local and global differential geometry. Applications of PDE to geometric problems including harmonic maps and minimal submanifolds. Geometric structures on manifolds. Symplectic and contact manifolds. Hamiltonian systems, metric geometry. Connections with sections 4, 6, 7, 8, 9, 10, 11 6. Topology Algebraic, differential, geometric and low dimensional topology. 4-manifolds and Seiberg-Witten theory. 3-manifolds including knot theory. Connections with sections 2, 4, 5, 7, 11 7. Lie Groups and Lie Algebras Algebraic groups, Lie groups and Lie algebras, including infinite dimensional ones, e.g. Kac-Moody, representation theory. Automorphic forms over number fields and function fields, including Langlands* program. Quantum groups. Shimura varieties. Vertex operator algebras. Enveloping algebras. Super algebras. Connections with sections 2, 3, 4, 5, 6, 8, 9, 11, 13 8. Analysis Classical and Fourier analysis, operator algebras, functional analysis, complex analysis. Connections with sections 5, 7, 9, 10, 11 9. Ordinary Differential Equations and Dynamical Systems Topological aspects of dynamics. Geometric and qualitative theory of ODE and smooth dynamical systems, bifurcations, singularities (including Lagrangian singularities), one-dimensional and holomorphic dynamics, ergodic theory (including sensitive attractors) Connections with sections 5, 7, 8, 11, 12, 17 10. Partial Differential Equations (includes non-linear functional analysis) Solvability, regularity and stability of equations and systems. Geometric properties (singularities, symmetry). Variational methods. Spectral theory, scattering, inverse problems. Relations to continuous media and control. Connections with sections 5, 8, 11, 16 11. Mathematical Physics (joint piece with #4) Quantum mechanics. Operator algebras. Quantum field theory. General relativity. Statistical mechanics and random media. Integrable systems. Connections with sections 5, 6, 7, 8, 9, 10 12. Probability and Statistics Classical probability theory, limit theorems and large deviations. Combinatorial probability and stochastic geometry. Stochastic analysis. Random fields and multicomponent systems. Statistical inference, sequential methods and spatial statistics. Applications. Connections with sections 8, 9, 10, 11, 13, 14, 16, 17 13. Combinatorics Interaction of combinatorics with algebra, representation theory, topology, etc. Existence and counting of combinatorial structures. Graph theory. Finite geometries. Combinatorial algorithms. Combinatorial geometry. Connections with sections 1, 2, 3, 4, 7, 12 14. Mathematical Aspects of Computer Science (joint with IUCSI) Complexity theory and efficient algorithms. Parallelism. Formal languages and mathematical machines. Cryptography. Semantics and verification of programs. Computer aided conjectures testing and theorem proving. Symbolic computation. Quantum computing. Connections with sections 1, 2, 3, 4, 12 15. Numerical Analysis & Scientific Computing Difference methods, finite elements. Approximation theory. Computational applications of analysis. Optimization theory. Matrix calculations. Signal processing. Simulations and applications. Connections with sections 12, 17 16. Applications: a) applications applications of mathematics in other sections; topics and speakers to be developed in consultation with panels in other sections. Connections with sections 10, 12 b) (non-continuum) applied area, (for example. mathematics of communications & networking or an area of mathematical biology) topic and panelists to be determined in consultation with CICIAM c) materials/hydrodynamics 17. Control Theory and Optimization (joint with Mathematical Programming Society) Control, optimization and variational techniques. Linear, integer and non-linear programming, graph, and networks. Applications. Robotics. Connections with sections 9, 12, 15 18. Teaching and Popularization of Mathematics 19. History of Mathematics ------------------------------------------------------------------- See http://elib.zib.de:8000/CICM98 for details @@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@ Communicated by _SAC_COMMANDO_

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