2018 DST-ICTP-IMU Ramanujan Prize for Young Mathematicians from Developing Countries
jointly awarded by
- The Abdus Salam International Center for Theoretical Physics,
- The Department of Science and Technology (DST, Government of India), and
- The International Mathematical Union (IMU).
It is our pleasure to announce that the winner of the 2018 Ramanujan Prize for Young Mathematicians from Developing Countries is Ritabrata Munshi of the Indian Statistical Institute, Kolkata, India and the Tata Institute of Fundamental Research, Mumbai, India.
The prize is in recognition of Munshi's outstanding work in Number Theory.
More specifically, Ritabrata Munshi has made profound contributions to analytic number theory, in particular to the study of analytic properties of L-functions and automorphic forms. L-functions were defined in great generality by Robert Langlands, and while much is known about them from the representation theoretic and arithmetic geometry points of view, their deeper analytic properties are largely unknown.
In recent years, the work of Henryk Iwaniec and his collaborators has started to shed light on growth properties of these L-functions in the case of the group GL(2) proving what are now called subconvexity theorems. These theorems, which are actually estimates for the L-function on the "critical" line, represent progress towards the proof of the Lindelof hypothesis, which is one of the big open problems in analytic number theory, perhaps second only to the Riemann hypothesis.
Munshi takes these techniques to new levels by proving subconvexity theorems for some L-functions that come from GL(3). In a series of remarkable papers he has extended the reach of the classical Hardy-Littlewood-Ramanujan "circle method" to obtain sharp subconvexity estimates for L-functions arising from cusp forms on higher rank groups.
The progress from GL(2) to GL(3) is very hard-won and involves a lot of technical prowess as well as ingenuity. While many authors have established some special cases, Ritabrata's results are perhaps the most far-reaching and most general. In addition, he has made striking contributions to other areas in number theory like Diophantine equations, quadratic forms and elliptic curves. His work also makes clear that he is far from done, and that we should expect to see many more interesting results from him in the future.
The selection committee consisted of Rajendra Bhatia, Alicia Dickenstein, Stefano Luzzatto (chair), Philibert Nang and Van Vu.