# 2024 CRM-Fields-PIMS Prize Awarded to Dr. Ram Murty of Queen's University

The winner of 2024 CRM-Fields-PIMS prize is Prof. Ram Murty, of Queenâ€™s University.

After completing his PhD at MIT in 1980 under the supervision of Harold Stark, and post-doctoral fellowships at the Tata Institute and at the Institute for Advanced Study, Ram Murty moved to McGill University in 1982, remaining there until 1996. In 1996, he moved to Queenâ€™s University, where he is now the A.V.Douglas Distinguished University Professor.

Ram Murty first came to prominence in the early 1980s with his breakthrough result (joint with Rajiv Gupta) on Artinâ€™s conjecture (that each prime multiplicatively generates infinitely many finite fields of prime order). This, and subsequent refinements, tell us that the conjecture holds for all but possibly two primes. This was followed by an analogous result for elliptic curves E defined over the rationals, showing that there is an infinitude of primes for which E(Fp) is cyclic. With his brother Kumar, he supplied the key result needed to make Kolyvaginâ€™s work on the rank 0 case of the Birch-Swinnerton-Dyer conjecture unconditional, showing that the central critical values of the Hasse-Weil L-series of an elliptic curve twisted by a quadratic Dirichlet character are non-zero for infinitely many such characters.

Other notable highlights include a clarification of a class of L-functions, the Selberg L-functions, which captures the desired properties of the L-functions which occur in the Langlands program; basic results on modular forms and their Fourier coefficients; and some striking transcendence results for special values of L-functions.

Ram Murty works on a wide front, with imagination and originality, combining both analytic and algebraic techniques and bringing real philosophical depth to the questions he considers. Few parts of the subject of number theory, including its ties to far-afield topics like mathematical logic, p-adic geometry, and foundations, have been left untouched by his wide-ranging intellectual curiosity.

The research presence of Ram Murty on the Canadian mathematical scene is far from being measured only by his own research publications. There is an impressive list of monographs that he has authored, which have served as both introductions and reference works to generations of scholars. Indeed, he has played an active role in forming the next generation of number theorists in Canada, India, and throughout the world, mentoring thirty-nine post-doctoral fellows and supervising over fifty PhD and Masterâ€™s theses. If not a Canadian record, it is close; and to this one should add his foundational role in several structural initiatives that have built up the strong Canadian number-theoretic school, such as Montrealâ€™s Centre Interuniversitaire en Calcul MathĂ©matique AlgĂ©brique (CICMA) lab and the very successful Canadian Number Theory Association (CNTA) conferences.

As a researcher, scholar, mentor, and indeed as a generator and focus of an extraordinary amount of mathematical activity, Ram Murty is a most worthy recipient of the 2024 CRM-Fields-PIMS prize.