Table of Contents

Determinacy and large cardinals; The art of ordinal analysis; Analytic difference rings; Borel superrigidity and the classification problem for the torsion-free abelian groups of finite rank; Zeta functions of groups and rings; On differential graded categories; Derived equivalences and finite dimensional algebras; Algorithmic and asymptotic properties of groups; A. unified approach to computations with permutation and matrix groups; Some results in noncommutative ring theory; Hecke orbits as Shimura varieties in positive characteristic; Heegner points, Stark-Heegner points and values of $L$-series; Galois deformations and arithmetic geometry of Shimura varieties; Generalising the Hardy-Littlewood method for primes; Aspects geometriques du Lemme Fondamental de Langlands-Shelstad; Equidistribution, $L$-functions and ergodic theory: on some problems of Yu. Linnik; $p$-adic motivic cohomology in arithmetic; Vanishing of $L$-functions and ranks of Selmer groups; Special values of $L$-functions modulo $p$; Evaluation maps, slopes, and algebraicity criteria; Derived categories of coherent sheaves; Invariants of singularities of pairs; Rational curves and rational points; Rigidity of rational homogeneous spaces; Geometry of multiple zeta values; Geometry over nonclosed fields; Algebraic Morse theory and the weak factorization theorem; Elliptic and parabolic problems in conformal geometry; The topology and geometry of contact structures in dimension three; Generalized triangle inequalities and their applications; The asymptotic geometry of negatively curved spaces: uniformization, geometrization and rigidity; Lagrangian submanifolds: from the local model to the cluster complex; Gromov-Witten invariants and moduli spaces of curves; Extremal metrics and stabilities on polarized manifolds; Tropical geometry and its applications; Embedded minimal surfaces; Floer homology in symplectic geometry and in mirror symmetry; Properly embedded minimal surfaces with finite topology; Applications of loop group factorization to geometric soliton equations; Non-positive curvature and complexity for finitely presented groups; Link homology and categorification; Curve complexes, surfaces and 3-manifolds; $mathbb{A}1$-algebraic topology; Development in symplectic Floer theory; Heegaard diagrams and Floer homology; The cohomology of automorphism groups of free groups; Spaces of quasi-maps into the flag varieties and their applications; On the local Langlands and Jacquet-Langlands correspondences; An invitation to bounded cohomology; Fibration de Hitchin et structure endoscopique de la formule des traces; Hecke algebras and harmonic analysis; Continuous representation theory of $p$-adic Lie groups; The algebraization of Kazhdan's property (T); Rankin-Selberg integrals, the descent method, and Langlands functorality; Representation theory and the cohomology of arithmetic groups; Some results on compactifications of semisimple groups; Local $Tb$ theorems and applications in PDE; Almost everywhere convergence and divergence of Fourier series; Iterated Segre mappings of real submanifolds in complex space and applications; Towards conformal invariance of 2D lattice models; Aspects of the $L2$-Sobolev theory of the $overlinepartial$-Neumann problem; Greedy approximations with regard to bases; Analytic capacity, rectifiability, and the Cauchy integral; Isomorphic and almost-isometric problems in high-dimensional convex geometry; Amenable actions and applications; Structure and classification of $Cast$-algebras; Convexity, complexity, and high dimensions; Higher index theory of elliptic operators and geometry of groups; Ergodic Ramsey theory: a dynamical approach to static theorems; Hyperbolic billiards and statistical physics; Some recent progress in geometric methods in the instability problem in Hamiltonian mechanics; Diagonalizable flows on locally homogeneous spaces and number theory; Author index; Newton interpolation polynomials, discretization method, and certain prevalent properties in dynamical systems; From combinatorics to ergodic theory and back again; From Brouwer theory to the study of homeomorphisms of surfaces; All, most, some differentiable dynamical systems; Geodesics on flat surfaces; Nonlinear Schrodinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problem; The periodic Lorentz gas in the Boltzmann-Grad limit; Conformal invariants and nonlinear elliptic equations; Asymptotic solutions for large time of Hamilton-Jacobi equations; The weak-coupling limit of large classical and quantum systems; Symmetry of entire solutions for a class of semilinear elliptic equations; Vortices in the Ginzburg-Landau model of superconductivity; Recent developments in elliptic partial differential equations of Monge-Ampere type; The initial value problem for nonlinear Schrodinger equations; Singular solutions of partial differential equations modelling chemotactic aggregation; Matrix ansatz and large deviations of the density in exclusion processes; Correlation functions of the $XXZ$ Heisenberg spin chain: Bethe anastz approach; Gromov-Witten invariants and topological strings: a progress report; The Cauchy problem in general relativity; Categorification and correlation functions in conformal field theory; Soliton dynamics and scattering; Hypocoercive diffusion operators; On Ising droplets; Simple random covering, disconnection, late and favorite points; Modelling genes: mathematical and statistical challenges in genomics; Geometric stochastic analysis on path spaces; Statistical challenges with high dimensionality: feature selection in knowledge discovery; Random matrices and enumeration of maps; The weak/strong survival transition on trees and nonamenable graphs; New developments in stochastic dynamics; Stochastic classification models; Random partitions and instanton counting; Estimation in inverse problems and second-generation wavelets; Conformal restriction properties; Rational and algebraic series in combinatorial enumeration; Towards a structure theory for matrices and matroids; Cherednik algebras, Macdonald polynomials and combinatorics; Poisson cloning model for random graphs; Randomness and regularity; Additive combinatorics and geometry of numbers; Geometric bistellar flips: the setting, the context and a construction; A survey of Pfaffian orientations of graphs; The additivity problem in quantum information theory; Complex networks and decentralized search algorithms; On expander graphs and connectivity in small space; Potential functions and the inefficiency of equilibria; Sublinear time algorithms; Pseudorandomness and combinatorial constructions; A posteriori error analysis and adaptive methods for partial differential equations; Error estimates for anisotropic finite elements and applications; Linear subdivision schemes for the refinement of geometric objects; Wave propagation software, computational science, and reproducible research; Reduced basis method for the rapid and reliable solution of partial differential equations; Finite element algorithms for transport-diffusion problems: stability, adaptivity, tractability; Convex optimization of graph Laplacian eigenvalues; Controllability of evolution equations of fluid dynamics; Port-Hamiltonian systems: an introductory survey; Passive linear discrete time-invariant systems; Control and numerical approximation of the wave and heat equations; Compressive sampling; Total variation based image denoising and restoration; A wavelet based sparse grid method for the electronic Schrodinger equation; Mathematical and numerical analysis for molecular simulation: accomplishments and challenges; Evolutionary dynamics of cooperation; Fractional Brownian motion: stochastic calculus and applications; Atomistic and continuum models for phase change dynamics; Understanding and misunderstanding the Third International Mathematics and Science Study: what is at stake and why K-12 education studies matter; Mathematics, the media, and the public; Panel A: Controversial issues in K-12 mathematical education; Panel B: What are PISA and TIMSS? What do they tell us?; Panel C: The role of mathematicians in K-12 mathematics education; Method versus calculus in Newton's criticisms of Descartes and Leibniz; Author index