Analytic number theory was born out of an effort to understand how prime numbers are distributed. This had led to the discovery of the wide-ranging and profound theories of L-functions, sieves, and pretentious multiplicative functions, all of which have now become fields of research of their own with intensive activity. In addition, there are important connections of analytic number theory with additive combinatorics, probability theory and ergodic theory. The interplay between these fields has been key to understanding prime numbers and the multiplicative structure of the integers.

Analytic number theory has witnessed a remarkable number of breakthroughs in the recent few years. A testament to this progress is James Maynard’s 2022 Fields Medal for his "spectacular contributions to analytic number theory, particularly in understanding prime numbers and Diophantine approximation", as well as the 2023 Cole Prize of Kaisa Matomäki and Maksym Radziwiłł for their spectacular development of multiplicative functions in very short intervals. This Thematic Program at the Fields Institute will celebrate these and other advances while at the same time setting the ground for new directions of research. This program will incorporate the Fields Medal Symposium on Maynard’s work, which is scheduled to take place in Fall 2028.