2013; 824 pp; hardcover ISBN13: 9783037191200 List Price: US$128 Member Price: US$102.40 Order Code: EMSEMC/2012
 The European Congress of Mathematics, held every four years, has become a wellestablished major international mathematical event. Following those in Paris (1992), Budapest (1996), Barcelona (2000), Stockholm (2004), and Amsterdam (2008), the Sixth European Congress of Mathematics (6ECM) took place in Kraków, Poland, July 27, 2012, with about 1000 participants from all over the world. Ten plenary, thirtythree invited lectures, and three special lectures formed the core of the program. As at all the previous EMS congresses, ten outstanding young mathematicians received the EMS prizes in recognition of their research achievements. In addition, two more prizes were awarded: the Felix Klein Prize for a remarkable solution of an industrial problem, andfor the first timethe Otto Neugebauer Prize for a highly original and influential piece of work in the history of mathematics. The program was complemented by twentyfour minisymposia with nearly 100 talks that covered all areas of mathematics. Six panel discussions were organized, covering a variety of issues ranging from the financing of mathematical research to gender imbalance in mathematics. These proceedings, which present extended versions of most of the invited talks delivered during the congress, provide a permanent record of the best of what mathematics offers today. Readership Graduate students and research mathematicians. Table of Contents Plenary Lectures  A. Constantin  Some mathematical aspects of water waves
 C. De Lellis and L. Székelyhidi  Continuous dissipative Euler flows and a conjecture of Onsager
 H. Edelsbrunner and D. Morozov  Persistent homology: theory and practice
 M. Gromov  In a search for a structure, Part 1: On entropy
 C. Hacon  Classification of algebraic varieties
 A. Braverman and D. Kazhdan  Representations of affine KacMoody groups over local and global fields: A survey of some recent results
 S. Serfaty  Emergence of the Abrikosov lattice in several models with two dimensional Coulomb interaction
 S. Shelah  Dependent classes, E72
 M. Talagrand  Chaining and the geometry of stochastic processes
Invited Lectures  A. Alekseev  Duflo isomorphism, the KashiwaraVergne conjecture and Drinfeld associators
 J. Bertoin  Coagulation with limited aggregations
 S. Cantat  The Cremona group in two variables
 V. Caselles  Variational models for image inpainting
 A. Celletti  KAM theory and its applications: From conservative to dissipative systems
 P. Colmez  Le programme de Langlands padique
 T. Coates, A. Corti, S. Galkin, V. Golyshev, and A. Kasprzyk  Mirror symmetry and Fano manifolds
 H. Esnault  On flat bundles in characteristic \(0\) and \(p \gt 0\)
 A. A. Gaifullin  Combinatorial realisation of cycles and small covers
 I. Gallagher  Remarks on the global regularity for solutions to the incompressible NavierStokes equations
 O. Häggström  Why the empirical sciences need statistics so desperately
 A. Iserles  Computing the Schrödinger equation with no fear of commutators
 A. S. Kechris  Dynamics of nonarchimedean Polish groups
 B. Keller  Cluster algebras and cluster monomials
 S. Kołodziej  Weak solutions to the complex MongeAmpère equation
 G. Kozma  Reinforced random walk
 F. Merle  On blowup curves for semilinear wave equations
 A. E. Mironov  Commuting higher rank ordinary differential operators
 D. Nualart  Stochastic calculus with respect to the fractional Brownian motion
 A. Olevskii  Sampling, interpolation, translates
 L. Parnovski  Multidimensional periodic and almostperiodic spectral problems
 B. Schlein  Effective equations for quantum dynamics
 P. Śniady  Combinatorics of asymptotic representation theory
 H. Jia and V. Sveřák  On scaleinvariant solutions of the NavierStokes equations
 S. Todorčević  Ramseytheoretic analysis of the conditional structure of weaklynull sequences
Prize Winners' Lectures  S. Brendle  Uniqueness results for minimal surfaces and constant mean curvature surfaces in Riemannian manifolds
 A. Figalli  Stability in geometric and functional inequalities
 A. Ioana  Classification and rigidity for von Neumann algebras
 M. Lewin  A nonlinear variational problem in relativistic quantum mechanics
 C. Manolescu  Grid diagrams in Heegaard Floer theory
 G. Miermont  Random maps and continuum random \(2\)dimensional geometries
 T. Sanders  Approximate (Abelian) groups
 C. Ulcigrai  Shearing and mixing in parabolic flows
 E. Trelat  Optimal control theory and some applications to aerospace problems
 J. P. Hogendijk  Mathematics and geometric ornamentation in the medieval Islamic world
Special Lectures  J. F. Rodrigues  Some mathematical aspects of the Planet Earth
 P. Welch  Turing's mathematical work
 A. Siemaszko and M. P. Wojtkowski  Counting Berg partitions via Sturmian words and substitution tilings
