Andrew Granville (UCL)
Expanding pretension in analytic number theory

John Coates (Cambridge)
Quadratic twists of elliptic curves

Ariel Pacetti (Buenos Aires)
Constructing Heegner points when the "Heegner hypothesis" is not satisfied

Rob de Jeu (Amsterdam)
On K_2 of curves

Tim Dokchitser (Bristol)
Local arithmetic of hyperelliptic curves

Adam Harper (Cambridge)
Prime Number Races with very many competitors

Andrew Wiles (Oxford)
Class numbers of imaginary quadratic fields

Jack Thorne (Cambridge)
Galois representations attached to cohomological automorphic forms

Netan Dogra (Oxford)
A quadratic Chabauty's method for rational points on higher genus curves

Henri Johnston (Exeter)
Applications of hybrid p-adic group rings and hybrid Iwasawa algebras to arithmetic conjectures

John Cremona (Warwick)
Some density results in number theory

Luis Garcia (Imperial College London)
Regularized theta lifts and currents on orthogonal Shimura varieties

Harald Helfgott (CNRS)
The ternary Goldbach conjecture

Bruno Angles (Caen)
Units and Class Modules in the Arithmetic of Global Function Fields

Levent Alpoge (Cambridge)
The average elliptic curve has few integral points

Tommaso Centeleghe (Heidelberg)
On abelian varieties over F_p

Jan Vonk (Oxford)
Semi-stable reduction of correspondences

Jim Stankewicz (Bristol)
Torsion points on cm elliptic curves over prime degree fields

Lassina Dembélé (Warwick)
Supercuspidal types and the Jacquet-Langlands correspondence

Aurel Page (Warwick)
Computing Klein modular forms

Victor Abrashkin (Durham)
Galois groups of local fields, Lie algebras and ramification

Nigel Byott (Exeter)
Galois scaffolds and (generalised) Galois module structure

Nicolas Mascot (Warwick)
Computing modular Galois representations

Jack Thorne (Cambridge)
E_6 and integral points on genus 3 curves

Toby Gee (Imperial College London)
The weight part of Serre's conjecture

Efthymios Sofos (Bristol)
Counting rational points on smooth cubic surfaces