People

Jon Keating is a mathematician at the University of Oxford and the director of the collaboration. His research lies at the interface of number theory, random matrix theory and mathematical physics. With Nina Snaith he used random matrix theory to predict the moments of the Riemann zeta function, and with Yan Fyodorov and Ghaith Hiary he conjectured how the zeta function behaves near its largest values in short intervals. In the collaboration, he works on correlations and large values of L-functions.

Louis-Pierre Arguin is a mathematician at the City University of New York and the University of Oxford. A principal investigator of the collaboration, he is a probabilist whose research centres on log-correlated random fields, extreme value theory and spin glasses. His recent work applies these ideas to number theory, in particular to the Fyodorov–Hiary–Keating conjecture on the maximum of the Riemann zeta function in short intervals. In the collaboration, he works on the log-correlated structure of the zeta function and on the distribution of divisors.

Paul Bourgade is a mathematician at the Courant Institute of Mathematical Sciences, New York University, and a principal investigator of the collaboration. His research is in probability and mathematical physics, especially random matrix theory and the universality of eigenvalue statistics, log-correlated fields and Gaussian multiplicative chaos. In the collaboration, he works on the connections between random matrices and the Riemann zeta function, including its large values on the critical line, and on the probabilistic structure of the divisors of integers.

Adam Harper is a mathematician at the University of Warwick and a principal investigator of the collaboration. He works in analytic and probabilistic number theory, including random multiplicative functions, smooth numbers, and moments of the zeta function and of character sums. He showed that sums of random multiplicative functions exhibit better-than-squareroot cancellation, a phenomenon explained by multiplicative chaos. In the collaboration, he studies how log-correlated structure governs cancellation in sums of multiplicative functions and the moments of L-functions.

Dimitris Koukoulopoulos is a mathematician at the Université de Montréal and a principal investigator of the collaboration. His research is in analytic and multiplicative number theory, including the anatomy of integers, the distribution of primes and of multiplicative functions, and metric Diophantine approximation. With Terence Tao he obtained new bounds on the average of the Hooley Δ-function, a classical measure of how the divisors of an integer are spread out. In the collaboration, he works on the distribution of divisors and its links with sieve methods.

Kaisa Matomäki is a mathematician at the University of Turku and a principal investigator of the collaboration. She works in analytic number theory, especially multiplicative functions, primes in short intervals and correlations of multiplicative functions. With Maksym Radziwiłł she showed that multiplicative functions behave as expected in almost all short intervals, a result that opened new approaches to the Chowla conjecture. In the collaboration, she works on short-interval problems, the optimal choice of mollifiers and moments of L-functions.

James Maynard is a mathematician at the University of Oxford and a principal investigator of the collaboration. His research is in analytic number theory and centres on the distribution of prime numbers, including small and large gaps between primes, sieve methods, primes in special sequences and Diophantine approximation. With Kevin Ford he recently developed a new framework for analysing prime-detecting sieves. In the collaboration, he works on understanding the limits of sieve methods and on finding primes in new sequences.

Maksym Radziwiłł is a mathematician at New York University and a principal investigator of the collaboration. He works in analytic number theory, including multiplicative functions in short intervals, the value distribution and moments of L-functions, and the zeros of the Riemann zeta function. With Kaisa Matomäki he determined the behaviour of multiplicative functions in almost all short intervals. In the collaboration, he works on the Chowla conjecture, on mollifiers and zeros of the zeta function on the critical line, and on moments of L-functions.

Peter Sarnak is a mathematician at the Institute for Advanced Study and Princeton University and a principal investigator of the collaboration. His research spans number theory, analysis and mathematical physics, including automorphic forms, spectral theory, quantum chaos and the statistics of zeros of L-functions. With Nicholas Katz he developed the random matrix model for families of L-functions. In the collaboration, he works on the distribution of rational and integral points on varieties and on the links between random matrices and arithmetic.

Will Sawin is a mathematician at Princeton University and a principal investigator of the collaboration. He works in number theory and arithmetic geometry, using geometric and topological methods to study arithmetic statistics, especially over function fields. With Melanie Matchett Wood he developed a general moment framework for distributions of random algebraic structures, with applications to Galois groups and random 3-manifolds. In the collaboration, he works on function-field analogues of the ratios conjectures and on the statistics of arithmetic objects.

Kannan Soundararajan is a mathematician at Stanford University and a principal investigator of the collaboration. His research is in analytic number theory, including moments and extreme values of L-functions, multiplicative functions and the distribution of prime numbers. With Maksym Radziwiłł he developed mollifiers modelled on the Brun sieve, with applications to fractional moments of L-functions and to Tate–Shafarevich groups of elliptic curves. In the collaboration, he works on moments, mollifiers and the large values of L-functions.

Melanie Matchett Wood is a mathematician at Harvard University and a principal investigator of the collaboration. Her research lies at the crossroads of number theory, arithmetic geometry and probability, especially the distributions of random groups, Cohen–Lenstra heuristics and arithmetic statistics. With Will Sawin she developed a general moment framework for distributions on discrete algebraic structures. In the collaboration, she works on class groups and random groups, and on when independence heuristics in arithmetic can be justified.

[Short research summary]

[Short research summary]