Structure versus Randomness: a dichotomy in number theory

Overview

Save the date for February’s Trinity Research Talk, to be given by Dr Aled Walker (2010).

 

Dr Aled Walker received his doctorate in 2018 at the University of Oxford, under the supervision of Professor Ben Green. During that time he was awarded the Edward Gibbon Prize by Magdalen College, for his research communication. Since then, in addition to a Title A Fellowship at Trinity, he has held a Postdoctoral Fellowship at the Centre de Recherches Mathématiques in Montréal and a Junior Fellowship at Institut Mittag-Leffler in Stockholm.

 

In his thesis, Aled looked for new ways to use techniques from a relatively young mathematical field — known as ‘additive combinatorics’ — to understand classical questions about prime numbers. In this endeavour, it turns out that the following is a central question: is the collection of whole numbers that one is studying ‘structured’, or is it ‘pseudorandom’? In his talk, Aled will describe the meaning of these notions from first principles, and in doing so will touch on the work of at least 8 current or former Trinity Fellows, spanning over 100 years of research.