This is the second volume of the procedings of the second European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners. Together with volume II it contains a collection of contributions by the invited lecturers. Finally, volume II also presents reports on some of the Round Table discussions. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: Vol. I: N. Alon, L. Ambrosio, K. Astala, R. Benedetti, Ch. Bessenrodt, F. Bethuel, P. Bjørstad, E. Bolthausen, J. Bricmont, A. Kupiainen, D. Burago, L. Caporaso, U. Dierkes, I. Dynnikov, L.H. Eliasson, W.T. Gowers, H. Hedenmalm, A. Huber, J. Kaczorowski, J. Kollár, D.O. Kramkov, A.N. Shiryaev, C. Lescop, R. März. Vol. II: J. Matousek, D. McDuff, A.S. Merkurjev, V. Milman, St. Müller, T. Nowicki, E. Olivieri, E. Scoppola, V.P. Platonov, J. Pöschel, L. Polterovich , L. Pyber, N. Simányi, J.P. Solovej, A. Stipsicz, G. Tardos, J.-P. Tignol, A.P. Veselov, E. Zuazua.

Inhalt

Geometric set systems.- Recent developments in symplectic topology.- K-theory and algebraic groups.- Surprising geometric phenomena in high-dimensional convexity theory.- Microstructures, phase transition and geometry.- Different types of non-uniform hyperbolicity for interval maps are equivalent.- Metastability and typical exit paths in stochastic dynamics.- Rationality problems for group varieties.- Precise measurements in symplectic topology.- Nonlinear partial differential equations, Birkhoff normal forms, and KAM theory.- Group enumeration and where it leads us.- Studying dynamical systems with algebraic tools.- Mathematical results on the structure of large atoms.- Geography of irreducible 4-manifolds.- Transversals of d-intervals - comparing three approaches.- Algebras with involution and classical groups.- Huygens#x2019;principle and integrability.- Some problems and results on the controllability of partial differential equations.- Round Tables.- (A) Electronic literature in mathematics.- (B) Mathematical Games.- (D) Women and mathematics.- (E) Public image of mathematics.- (G) Education.