Invited Talks -- Computing Pro-P Galois Groups -- The Elliptic Curve Database for Conductors to 130000 -- On the Computation of the Coefficients of a Modular Form -- Cohen–Lenstra Heuristics of Quadratic Number Fields -- Algebraic Number Theory -- An Algorithm for Computing p-Class Groups of Abelian Number Fields -- Computation of Locally Free Class Groups -- Numerical Results on Class Groups of Imaginary Quadratic Fields -- Cyclic Polynomials Arising from Kummer Theory of Norm Algebraic Tori -- The Totally Real Primitive Number Fields of Discriminant at Most 109 -- A Modular Method for Computing the Splitting Field of a Polynomial -- Analytic and Elementary Number Theory -- On the Density of Sums of Three Cubes -- The Mertens Conjecture Revisited -- Fast Bounds on the Distribution of Smooth Numbers -- Use of Extended Euclidean Algorithm in Solving a System of Linear Diophantine Equations with Bounded Variables -- The Pseudosquares Prime Sieve -- Doubly-Focused Enumeration of Pseudosquares and Pseudocubes -- Lattices -- Practical Lattice Basis Sampling Reduction -- LLL on the Average -- On the Randomness of Bits Generated by Sufficiently Smooth Functions -- Curves and Varieties over Fields of Characteristic Zero -- Computing a Lower Bound for the Canonical Height on Elliptic Curves over ? -- Points of Low Height on Elliptic Curves and Surfaces I: Elliptic Surfaces over  with Small d -- Shimura Curves for Level-3 Subgroups of the (2,3,7) Triangle Group, and Some Other Examples -- The Asymptotics of Points of Bounded Height on Diagonal Cubic and Quartic Threefolds -- Testing Equivalence of Ternary Cubics -- Classification of Genus 3 Curves in Special Strata of the Moduli Space -- Heegner Point Computations Via Numerical p-Adic Integration -- Symmetric Powers of Elliptic Curve L-Functions -- Determined Sequences, Continued Fractions, and Hyperelliptic Curves -- Computing CM Points on Shimura Curves Arising from Cocompact Arithmetic Triangle Groups -- Arithmetic of Generalized Jacobians -- Hidden Pairings and Trapdoor DDH Groups -- Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10 -- Fast Bilinear Maps from the Tate-Lichtenbaum Pairing on Hyperelliptic Curves -- High Security Pairing-Based Cryptography Revisited -- Efficiently Computable Endomorphisms for Hyperelliptic Curves -- Construction of Rational Points on Elliptic Curves over Finite Fields -- 20 Years of ECM -- Discrete Logarithms -- An Index Calculus Algorithm for Plane Curves of Small Degree -- Signature Calculus and Discrete Logarithm Problems -- Spectral Analysis of Pollard Rho Collisions -- Hard Instances of the Constrained Discrete Logarithm Problem.