The purpose of this workshop is to honour the 70th birthday of Professor Roger Heath-Brown FRS, which takes place on 12th October 2022. Professor Heath-Brown has been a leading figure in analytic number theory for over fifty years. He has more than 180 publications since 1974, and nearly 3000 citations, by over 1000 authors. These are monumental numbers by the standards of pure mathematics. During the course of his career, Professor Heath-Brown has revolutionised many different branches of analytic number theory, inspiring new generations of number theorists to go further than ever before. His research is studded with gems, whose impact is still reverberating in modern day research.