Proceedings Of International Congress Of Mathematicians

Contents 1 Logic and foundations Rod Downey Algorithmic randomness and computability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Itay Neeman Determinacy and large cardinals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Michael Rathjen The art of ordinal analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Thomas Scanlon Analytic difference rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Simon Thomas Borel superrigidity and the classification problem for the torsion-free abelian groups of finite rank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 2 Algebra William Crawley-Boevey Quiver algebras, weighted projective lines, and the Deligne–Simpson problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Marcus du Sautoy* and Fritz Grunewald* Zeta functions of groups and rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 Bernhard Keller On differential graded categories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 Raphaël Rouquier Derived equivalences and finite dimensional algebras . . . . . . . . . . . . . . . . . . . . . . . 191 Mark Sapir Algorithmic and asymptotic properties of groups . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Ákos Seress A unified approach to computations with permutation and matrix groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 Agata Smoktunowicz Some results in noncommutative ring theory . . . . . . . . .