Harald Bohr Lecture: James Maynard
Speaker: James Maynard (Professor at the University of Oxford).
Title: Prime numbers and zero densities.
Abstract: The Riemann Hypothesis, often considered one of the most important open problems in mathematics, would have a number of fantastic consequences for our understanding of the distribution of prime numbers. It claims that all the (non-trivial) zeros of a complex function (the Riemann zeta function) have real part equal to 1/2. However, it turns out that several of these consequences would actually follow from a weaker 'zero density' result that says 'most' zeros lie 'close' to the line with real part equal to 1/2. I'll describe this picture, as well as recent work (joint with Larry Guth) that improves an 80-year-old estimate on the density of zeros, with corresponding improvements for the distribution of primes.
James Maynard is a Professor at the University of Oxford and is one of the leading figures in the field of number theory. His work continues to offer new insights into some of the most profound and elusive problems in mathematics.
The prime numbers are fascinating and mysterious integers which have startled mathematicians since antiquity. Maynard has repeatedly expanded our knowledge about these numbers, for instance by showing
- that there are many small gaps between primes, getting us closer to understanding the twin prime conjecture and its generalizations,
- that there are large gaps between primes, resolving a long-standing conjecture of Erdös,
- there are infinitely many primes that avoid any given digit in its decimal expansion, as well as similar results in other bases.
Similarly, Maynard has made spectacular advances in the field of Diophantine approximation. This field tries to understand basic questions about how well real numbers can be approximated by rational numbers. Together with his collaborators, Maynard has proved the Duffin-Schaeffer conjecture which gives precise conditions that determine whether the set of real numbers satisfying a certain approximation condition has full Lebesgue measure.
Maynard is a fellow of the Royal Society and has been awarded numerous prizes, including the SASTRA Ramanujan Prize (2014), an LMS Whitehead Prize (2015), an EMS Prize (2016), the Compositio Prize (2016), the AMS Cole Prize (2020) and a New Horizons Prize (2023).
In 2022 Maynard was awarded the Fields Medal for “contributions to analytic number theory, which have led to major advances in the understanding of the structure of prime numbers and in Diophantine approximation”.
Morten S. Risager
There will be coffee & cakes before the lecture, at 15:00 in front of Auditorium 1.