Proceedings of the International Congress of Mathematicians

the cube
- Applications dont la source est un classifiant
- Spaces of algebraic cycles: Levels of holomorphic approximation
- Dehn surgery on knots in the 3-sphere
- Cyclic splittings of finitely presented groups and the canonical JSJ-decomposition
- An algorithm to recognize the 3-sphere
- Characteristic classes, lattice points, and Euler-MacLaurin formulae
- Positive scalar curvature metrics - Existence and classification questions
- Nonlocally linear manifolds and orbifolds

Section 6. Algebraic geometry
- Mumford-Stabilität in der algebraischen Geometrie
- Fundamental groups of curves in characteristic p
- Mixed motives, motivic cohomology, and Ext-groups
- Rational curves on algebraic varieties
- Some Eisenstein cohomology classes for the integral unimodular group
- Rigid and exceptional vector bundles and sheaves on a Fano variety
- Variations of Hodge structure and algebraic cycles

Section 7. Lie groups and representations
- Genuine representations of the metaplectic group and epsilon factors
- The irreducible characters for semi-simple algebraic groups and for quantum groups
- Automorphic forms on Os+2,2(?)+ and generalized Kac-Moody algebras
- Spherical varieties
- Rigidity properties of group actions on CAT(0)-spaces
- Smooth representations of p-adic groups: The role of compact open subgroups
- Flows on homogeneous spaces and diophantine approximation
- Singular automorphic forms
- Gradings on representation categories
- Comparaison d'integrales orbitales pour des groupes p-adiques

Section 8. Real and complex analysis
- L2-methods and effective results in algebraic geometry
- Meromorphic functions: Progress and problems
- Teichmüller space, dynamics, probability
- Fibering compact Kähler manifolds over projective algebraic varieties of general type
- Regularity of Fourier integral operators
- Finding structure in sets with little smoothness
- Topological, geometric, and complex analytic properties of Julia sets
- Smoothing estimates for the wave equation and applications
- A survey of Möbius groups
- Geometric and dynamical aspects of real submanifolds of complex space

Section 9. Operator algebras and functional analysis
- The classification problem for amenable C*-algebras
- Recent results in the theory of infinite-dimensional Banach spaces
- Exact C*-algebras, tensor products, and the classification of purely infinite algebras
- Distortion and stabilized structure in Banach spaces; New geometric phenomena for Banach and Hilbert spaces
- Operator algebras and conformal field theory
- The algebra of functional analysis (Manuscript not submitted)

Section 10. Probability and statistics
- Brownian motion, heat kernels, and harmonic functions
- Interaction and hierarchy in measure-valued processes
- Abstract statistical estimation and modern harmonic analysis
- Probabilistic methods in finance (Manuscript not submitted)
- Parabolic systems in random media and aspects of intermittency (Manuscript not submitted)
- Quasi-regular Dirichlet forms and applications
- A surface view of first-passage percolation
- Quantum stochastic calculus
- Measure-valued branching diffusions and interactions
- Diffusion processes in random environments

Section 11. Partial differential equations
- Analytical and numerical aspects of fluid interfaces
- Morse theory in differential equations
- Analyse microlocale et mécanique des fluides en dimension deux
- Some mathematical problems of fluid mechanics
- Hyperbolic systems of conservation laws
- Eigenfunctions and harmonic functions in convex and concave domains
- Singularities of solutions of nonlinear parabolic and elliptic equations (Manuscript not submitted)
- Kinetic equations and hyperbolic systems of conservation laws
- The Cauchy problem for harmonic maps on Minkowski space
- Interface dynamics in phase transitions
- Fully nonlinear elliptic equations and applications to geometry
- Lower-semicontinuity of variational integrals and compensated compactness

Section 12. Ordinary differential equations and dynamical systems
- The Riemann-Hilbert problem and Fuchsian differential equations on the Riemann sphere
- Invariant sets of hamiltonian systems and variational methods
- Rotation vectors for surface diffeomorphisms
- A priori estimates and regularity of nonlinear waves
- Applications of dynamics to compact manifolds of negative curvature
- On the borderline of real and complex dynamics
- Ergodic variational methods: new techniques and new problems
- Homoclinic bifurcations and persistence of nonuniformly hyperbolic attractors (Talk not delivered at the congress)
- Ergodic theory of attractors

Section 13. Mathematical physics
- Noncommutative geometry and the quantum Hall effect
- Conformal field theory and integrable systems associated to elliptic curves
- Free field realizations in representation theory and conformal field theory
- Homogenized models of strongly inhomogeneous media
- Fluxes and dimers in the Hubbard model
- Von Neumann algebras and quantum field theory
- Two-dimensional Yang-Mills theory and topological field theory
- Mirror symmetry and moduli spaces of superconformal field theories
- The critical behaviour of random systems
- A rigorous (renormalization group) analysis of superconducting systems

Section 14. Combinatorics
- Eigenvalues of graphs
- Extremal hypergraphs and combinatorial geometry
- Asymptotics of hypergraph matching, covering and coloring problems
- Combinatorics and convexity
- Probabilistic methods in combinatorics
- Asymptotic combinatorics and algebraic analysis

Section 15. Mathematical aspects of computer science
- Probabilistic proof systems
- The computational complexity of counting
- Methods for message routing in parallel machines
- Randomness and non determinism
- Pseudorandom generators for derandomization of algorithms (Manuscript not submitted)

Section 16. Numerical analysis and scientific computing
- Mathematical modeling and numerical analysis of linearly elastic shells
- Multiscale techniques - Some concepts and perspectives
- Matrix computation and the theory of moments
- Subscale capturing in numerical analysis
- Analysis-based fast numerical algorithms of applied mathematics
- Solving numerically Hamiltonian systems

Section 17. Applications of mathematics in the sciences
- Methods of control theory in nonholonomic geometry
- Homogenization, renormalization and the mathematics of inhomogeneous media (Manuscript not submitted)
- High-resolution computations of incompressible fluid flow (Manuscript not submitted)
- Whiskered tori and chaotic behavior in nonlinear waves
- Formulas for finding coefficients from nodes/nodal lines
- Mechanochemical energy conversion in biological systems (Talk not delivered at the congress and manuscript not submitted)
- Backward stochastic differential equations, and applications
- Max-plus algebra and applications to system theory and optimal control
- Statistical mechanics and hydrodynamical turbulence
- Spaces of observables in nonlinear control

Section 18. Teaching and popularization of mathematics
- Changes in the teaching of undergraduate mathematics: The role of technology
- Issues for the popularization of mathematics
- Number theory as a core mathematical discipline

Section 19. History of mathematics
- Mathematics in medieval Islamic Spain
- Mathematics in national contexts (1875-1900): An international overview
- Hermann Weyl's "Purely infinitesimal geometry"