会议名称(英文)： International Congress of Mathematicians 2014
所属学科： 基础数学,计算数学与科学工程计算,概率论与数理统计,应用数学,运筹学与控制论
开始日期： 2014-08-13
结束日期： 2014-08-21
所在国家： 韩国
所在城市： 韩国
具体地点： Coex , Seoul , Korea
主办单位： International Mathematical Union (IMU)
摘要截稿日期： 2014-02-28
论文录用通知日期： 2014-04-30
联系电话： +82-2-563-2014
传真： +82-2-563-2022
E-MAIL： icm@icm2014.org
会议网站： http://www.icm2014.org/
会议背景介绍：
The International Congress of Mathematicians (ICM) is the largest international congress in the mathematics community. It is held once every four years under the auspices of the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize, the Gauss Prize, and the Chern Medal are awarded during the opening ceremony on the first day of the congress. Each congress is memorialized by printed Proceedings recording academic papers based on invited talks intended to reflect the current state of the science.
The Korean mathematical community is delighted to host the next congress in Seoul, Korea in 2014. We will make every effort to make SEOUL ICM 2014 a turning point for mathematics; to reach out to the public and to be recognized and valued by society.
We welcome our colleagues from around the world to the Congress, and hope that you will also be able to savor some of the fine attractions that our country offers. Korea, with a five-millennia-long history, is an attractive place to visit and has its own unique cultural heritage, distinct from that of other Asian countries. A visit to the country's numerous historical relics, ten of which are designated UNESCO World Cultural Heritage Sites, will make ICM participants' journey all the more special.
征文范围及要求：
The following subject areas have been chosen for ICM 2014 (section descriptions as well as the number of plenary and invited lectures to be given in each section):
1. Logic and Foundations (3-5 lectures)
Model theory. Set theory. Recursion theory. Proof theory. Applications.
Connections with sections 2, 3, 13, 14.
2. Algebra (4-6 lectures)
Groups (finite, infinite, algebraic) and their representations. Rings, Algebras and Modules (except as specified in other sections, Geometry, or Lie theory). Algebraic K-theory, Category theory, Computational aspect of algebra and applications.
Connections with sections 1, 3, 4, 5, 6, 7, 13, 14.
3. Number Theory (9-12 lectures)
Analytic and algebraic number theory. Local and global fields and their Galois groups. Zeta and L-functions. Diophantine equations. Arithmetic on algebraic varieties. Diophantine approximation, transcendental number theory, and geometry of numbers. Modular and automorphic forms, modular curves, and Shimura varieties. Langlands program. p-adic analysis. Number theory and physics. Computational number theory and applications, notably to cryptography.
Connections with sections 1, 2, 4, 7, 11, 12, 13, 14.
4. Algebraic and Complex Geometry (9-12 lectures)
Algebraic varieties, their cycles, cohomologies, and motives. Schemes. Geometric aspects of commutative algebra. Arithmetic geometry. Rational points. Low-dimensional varieties. Singularities and classification. Birational geometry. Moduli spaces and enumerative geometry. Derived categories. Abelian varieties. Transcendental methods, topology of algebraic varieties. Complex differential geometry, K?hler manifolds and Hodge theory. Relations with mathematical physics and representation theory. Real algebraic and analytic sets. Rigid and p-adic analytic spaces. Tropical geometry. Non-commutative geometry.
Connections with sections 2, 3, 5, 6, 7, 8, 11, 13, 14.
5. Geometry (10-13 lectures)
Local and global differential geometry. Non-linear and fully non-linear geometric PDE. Geometric flows. Geometric structures on manifolds. Riemannian and metric geometry. Geometric aspects of group theory. Conformal geometry, K?hler geometry, Symplectic and Contact geometry, Geometric rigidity, General Relativity.
Connections with sections 2, 4, 6, 7, 8, 9, 10, 11, 12, 16, 17.
6. Topology (9-11 lectures)
Algebraic Topology, Differential Topology, Geometric Topology, Floer and gauge theories, Low-dimensional manifolds including knot theory and connections with Kleinian groups and Teichmüller theory, Symplectic Geometry and contact manifolds, and Topological quantum field theories.
Connections with sections 2, 4, 5, 7, 8, 11.
7. Lie Theory and Generalizations (8-10 lectures)
Algebraic and arithmetic groups. Structure, geometry, and representations of Lie groups and Lie algebras. Related geometric and algebraic objects, e.g. symmetric spaces, buildings, vertex operator algebras, quantum groups. Non-commutative harmonic analysis. Geometric methods in representation theory. Discrete subgroups of Lie groups. Lie groups and dynamics, including applications to number theory.
Connections with sections 2, 3, 4, 5, 6, 8, 9, 11, 12, 13.
8. Analysis and its Applications (9-12 lectures)
Classical analysis. Real and Complex analysis in one and several variables, potential theory, quasiconformal mappings. Harmonic analysis. Linear and non-linear functional analysis, operator algebras, Banach algebras, Banach spaces. Non-commutative geometry, spectra of random matrices. Asymptotic geometric analysis. Metric geometry and applications. Geometric measure theory.
Connections with sections 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16.
9. Dynamical Systems and Ordinary Differential Equations (9-12 lectures)
Topological and symbolic dynamics. Geometric and qualitative theory of ODE and smooth dynamical systems, bifurcations and singularities. Hamiltonian systems and dynamical systems of geometric origin. One-dimensional and holomorphic dynamics. Strange attractors and chaotic dynamics. Multidimensional actions and rigidity in dynamics. Ergodic theory including applications to combinatorics and combinatorial number theory. Infinite dimensional dynamical systems and PDE.
Connections with sections 5, 7, 8, 10, 11, 12, 13, 15, 16.
10. Partial Differential Equations (9-12 lectures)
Solvability, regularity, stability and other qualitative properties of linear and non-linear equations and systems. Asymptotics. Spectral theory, scattering, inverse problems. Variational methods and calculus of variations. Geometric Evolution equations. Optimal transportation. Homogenization and multiscale problems. Relations to continuous media and control. Modeling through PDEs.
Connections with sections 5, 8, 9, 11, 12, 15, 16, 17.
11. Mathematical Physics (9-12 lectures)
Quantum mechanics. Quantum field theory including gauge theories. General relativity. Statistical mechanics and random media. Integrable systems. Supersymmetric theories. String theory. Fluid dynamics.
Connections with sections 4, 5, 6, 7, 8, 9, 10, 12.
12. Probability and Statistics (10-13 lectures)
Stochastic processes, Interacting particle systems, Random media, Random matrices, conformally invariant models, Stochastic networks, Stochastic geometry, Statistical inference, High-dimensional data analysis, Spatial methods.
Connections with sections 3, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17
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13. Combinatorics (8-10 lectures)
Combinatorial structures. Enumeration: exact and asymptotic. Graph theory. Probabilistic and extremal combinatorics. Designs and finite geometries. Relations with linear algebra, representation theory and commutative algebra. Topological and analytical techniques in combinatorics. Combinatorial geometry. Combinatorial number theory. Additive combinatorics. Polyhedral combinatorics and combinatorial optimization.
Connections with sections 1, 2, 3, 4, 7, 9, 12, 14.
14. Mathematical Aspects of Computer Science (6-8 lectures)
Complexity theory and design and analysis of algorithms. Formal languages. Computational learning. Algorithmic game theory. Cryptography. Coding theory. Semantics and verification of programs. Symbolic computation. Quantum computing. Computational geometry, computer vision.
Connections with sections 1, 2, 3, 4, 12, 13, 15.
15. Numerical Analysis and Scientific Computing (5-7 lectures)
Design of numerical algorithms and analysis of their accuracy, stability, and complexity. Approximation theory. Applied and computational aspects of harmonic analysis. Numerical solution of algebraic, functional, stochastic, differential, and integral equations. Grid generation and adaptivity.
Connections with sections 8, 9, 10, 12, 14, 16, 17.
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16. Control Theory and Optimization (5-7 lectures)
Minimization problems. Controllability, observability, stability. Robotics. Stochastic systems and control. Optimal control. Optimal design, shape design. Linear, non-linear, integer, and stochastic programming. Applications.
Connections with sections 9, 10, 12, 15, 17.
17. Mathematics in Science and Technology (8-10 lectures)
Mathematics applied to the physical sciences, engineering sciences, life sciences, social and economic sciences, and technology. Bioinformatics. Mathematics in interdisciplinary research. The interplay of mathematical modeling, mathematical analysis, and scientific computation, and its impact on the understanding of scientific phenomena and on the solution of real life problems.
Connections with sections 9, 10, 11, 12, 14, 15, 16.
18. Mathematics Education and Popularization of Mathematics (2 lectures plus 3 panel discussions)
All aspects of mathematics education, from elementary school to higher education. Mathematical literacy and popularization of mathematics.
19. History of Mathematics (3 lectures)
Historical studies of all of the mathematical sciences in all periods and cultural settings. |
