2022 Ribenboim Prize Awarded to Dimitris Koukoulopoulos

The Ribenboim Prize of the Canadian Number Theory Association is usually presented biennially for distinguished research in number theory by a mathematician who is Canadian (or has close connections to Canadian mathematics) and has received their Ph.D. in the last 12 years.  Due to the pandemic, the 2022 prize was awarded to Dimitris Koukoulopoulos  at the June 2024 meeting of the Canadian Number Theory Association (CNTA XVI).

Following his undergraduate degree at Aristotle University in Thessaloniki, Dimitris Koukoulopoulos completed his PhD at University of Illinois Urbana-Champaign in 2010 under the supervision of Kevin Ford. After holding a CRM-ISM postdoctoral fellowship for two years at the University of Montreal, he was hired permanently and is now the Courtois Chair in fundamental research. His interests lie in analytic, probabilistic and transcendental number theory, particularly the anatomy of integers, multiplicative functions and metric Diophantine approximation.

He is one of the leading experts on the multiplication table problem, showing that new phenomena emerge for 7 and more  dimensions, and working with Ford and Green, and with Tao, to get a much better understanding of Hooley’s Delta function (for example, disproving an old conjecture of Maier and Tenenbaum).

He gave an elementary “pretentious” proof of the prime number theorem which is as strong as the best results known using Riemann’s zeros, and has adapted these ideas to similar results in arithmetic progressions. In so doing, Koukoulopoulos found a shocking converse to the Selberg-Delange theorem, showing that if the mean value of a 1-bounded multiplicative function is small then it must pretend to be 0 or a twist of the Moebius function, now generalized to B-bounded functions with Soundararajan.

Dimitris is known for studying the notoriously complicated deterministic interactions between addition and multiplication of integers by relating the situation to a random process, which allows him to adapt and create powerful tools from probability to answer number theoretic questions. Dimitris is clearly one of the world leaders of this “hot area” in analytic number theory.

Dimitris is perhaps best-known for his resolution with James Maynard of the infamous Duffin-Schaeffer conjecture, determining when almost all real numbers can infinitely often be well approximated by reduced fractions. There were conferences focussed on the proof of this central 80 year old problem, an ICM speaking invitation, a Frontier of Science award, it was an important part of Maynard’s Fields medal citation and Dimitris even received a phone-call from the president of Greece!

Source: Canadian Number Theory Association