Proceedings Of International Congress Of Mathematicians

Contents 10 Ordinary differential equations and dynamical systems (continued) Robert Ghrist Braids and differential equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Anton Gorodetski, Brian Hunt and Vadim Kaloshin* Newton interpolation polynomials, discretization method, and certain prevalent properties in dynamical systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Bryna Kra From combinatorics to ergodic theory and back again . . . . . . . . . . . . . . . . . . . . . . . 57 Patrice Le Calvez From Brouwer theory to the study of homeomorphisms of surfaces . . . . . . . . . . 77 Michael Shub All, most, some differentiable dynamical systems . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Anton Zorich Geodesics on flat surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 11 Partial differential equations Stefano Bianchini Asymptotic behavior of smooth solutions for partially dissipative hyperbolic systems and relaxation approximation . . . . . . . . . . . . . . . . . . . . . . . . . . 147 Patrick Gérard Nonlinear Schrödinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problem . . . . . . . . . . . . . . . . . . . . . 157 François Golse The periodic Lorentz gas in the Boltzmann-Grad limit . . . . . . . . . . . . . . . . . . . . . . 183 Matthew J. Gursky Conformal invariants and nonlinear elliptic equations . . . . . . . . . . . . . . . . . . . . . . . 203 Hitoshi Ishii Asymptotic solutions for large time of Hamilton–Jacobi equations . . . . . . . . . . . 213 Mario Pulvirenti The weak-coupling limit of large