Weekend research talk: James Maynard on prime numbers at ICM 2022

Every four years, researchers from around the world gather at the International Congress of Mathematicians. Fields medals are awarded, and many lectures are given by the greatest experts in the world, aimed at a general audience of mathematicians.

A lecture at the ICM (typically given both as a live talk and as a longer and more comprehensive written survey) is more accessible than most regular research talks, but they also tend to give a broader overview of a research area in which the speaker is an expert.

Today I want to share the ICM 2022 lecture delivered by James Maynard, whom you may know from many Numberphile videos or from reading about the Fields medallists of 2022.

This lecture is hard to find, since it is embedded within a longer 8-hour video from the International Mathematical Union, but here it is, starting at 1:18:15 and ending at 2:21:20. He is introduced by Kannan Soundararajan, who gave the talk recommended here last week.

This is just a brilliant talk, that I would wholeheartedly recommend if you want to see one of the greatest prime number experts in the world share his unique perspective on the central problems of prime number theory. L-functions appear around 1:25:00 in the video, where he explains their role within the larger context of methods for "counting primes".

You may also enjoy the written version of the lecture, as well as the more elementary essay by Okounkov written on the occasion of Maynard's Fields medal.