April 27, 2018

# Professor Maksym Radziwill named recipient of the 2018 Coxeter-James Prize

OTTAWA – The Canadian Mathematical Society is pleased to announce that Professor Maksym Radziwill (McGill) has been named the recipient of the 2018 Coxeter-James Prize. Professor Radziwill will receive his award and present a prize lecture at the CMS Winter Meeting in Vancouver, British Columbia, December 7-10, 2018.

Professor Radziwill works in analytic number theory, focusing on the distribution of prime numbers, multiplicative functions and related objects. His list of publications includes his recent work with Matomaki on multiplicative functions in short intervals (Annals of Math, 2016), which establishes that if one picks at random a short string of consecutive integers then most of the time the multiplicative structure of the integers in the short interval resembles the multiplicative structure of the integers in the “long” interval starting at 1. In more technical terms, he showed that most of the time short averages of bounded multiplicative functions are close to long averages. This result goes beyond the capability of the Riemann Hypothesis. It led to the resolution of the Erdos discrepancy problem by Terence Tao, and to the first progress on Chowla’s conjecture. Chowla’s conjecture in its general form postulates a lack of correlation between the multiplicative structure of consecutive integers. As such its resolution is a necessary step on the path to the existence of twin primes. The work with Matomaki had also several other consequences: for instance it establishes the existence of smooth numbers (i.e integers composed of only small prime factors) between every C consecutive squares, where C is some large constant. This is related to the running time of Lenstra’s elliptic curve factoring algorithm. This work with Matomaki also opened the door for further progress on Sarnak’s conjecture on the lack of correlation of the Liouville function with sequences of topological entropy zero.

Radziwill also authored a paper with Soundararajan on “Moments and distribution of central values of quadratic twists of elliptic curves”, (Inventiones Math., 2015). This paper contains remarkable theorems on moments of quadratic twists of L functions of elliptic curves, with application to the distribution of sizes of Tate-Shafarevich groups. The techniques developed in this paper led to a better understanding of the distributional aspects of L-functions. For instance it led to a vastly simplified proof of Selberg’s central limit theorem for the Riemann zeta function and to the first distributional results resembling Selberg’s central limit theorem for discrete families of L-functions.

Radziwill has earned a number of honours and awards, namely the SASTRA Ramanujan Prize in 2016 with Matomaki, his work with Matomaki was the object of a Seminaire Bourbaki in 2016, in 2017 he was awarded the Sloan Fellowship. Radziwill was invited as a speaker at the International Mathematical Congress at Rio de Janeiro in 2018. He is currently a Canada Research Chair II at McGill University until 2021.

Radziwill earned his doctorate degree from Stanford University in 2013 (Advisor: Kannan Soundararajan). From 2014 to 2016 Radziwill served as the Hill Assistant Professor at Rutgers University and a member of the Institute for Advanced Study at Princeton University from 2013 to 2014. Currently, Professor Radziwill is an Assistant Professor at McGill University.

**About the Coxeter-James Prize**

The Coxeter-James Prize was inaugurated in 1978 to recognize young mathematicians who have made outstanding contributions to mathematical research. The award is named for two former CMS presidents, Donald Coxeter, who is recognized as one of the world’s best geometers, and Ralph Duncan James, who was a great contributor to mathematical development in Canada.

For information about past recipients visit: https://cms.math.ca/Prizes/info/cj.html

**About the Canadian Mathematical Society (CMS)**

The CMS is the main national organization whose goal is to promote and advance the discovery, learning and application of mathematics. The Society’s activities cover the whole spectrum of mathematics including: scientific meetings, research publications, and the promotion of excellence in mathematics competitions that recognize outstanding student achievements.

**For more information, please contact**:

Prof. Nantel Bergeron (York) Chair, CMS Research Committee Canadian Mathematical Society bergeron@yorku.ca 416-736-5250 |
Or |
Patricia Dack Fundraising and Communications Officer Canadian Mathematical Society pdack@cms.math.ca 613-733-2662 ext. 728 |