New Trends in Analytic Number Theory

Analytic number theory is the branch of mathematics in which ideas and methods of real and complex analysis are brought to bear on problems about integer numbers.  In particular, analytic techniques have led to major advances in number theory and helped to solve several important and difficult questions about integers.  In the last few years, analytic number theory has flourished and we have seen an upsurge of activity worldwide related to analytic number theory, prime number theory, and solutions to equations.

This research school will focus on three major advances that have emerged in the last few years:  prime number theory, number theory in function fields, and the Hardy and Littlewood Circle Method and Diophantine Geometry.  Several recent results in these areas represent new trends in analytic number theory and the lecture courses aim to offer a gentle introduction to these exciting developments. 

Pretentiousness in Analytic Number Theory
Lecturer:  Andrew Granville (UCL)

Topics in Classical Analytic Number Theory
Lecturer: Steve Gonek (Rochester)

Number Theory in Function Fields
Lecturers: Jon Keating (Bristol) and Zeev Rudnick (Tel Aviv)

Hardy and Littlewood Circle Methods and Vinogradov's Mean Value Theorem
Lecturer: Trevor Wooley (Bristol)

To complement the mini-courses, there will be guest lectures from Chris Hughes (York), James Maynard (Oxford), Damaris Schindler (Utrecht) and Caroline Turnage-Butterbaugh (Duke).