Arul Shankar

Arul Shankar is an Indian mathematician at the University of Toronto specialising in number theory; more specifically, arithmetic statistics. He obtained his PhD from Princeton University in 2012 under Manjul Bhargava.[1] Shankar is known for his work, with Manjul Bhargava, establishing unconditionally that the average rank of elliptic curves is bounded when ordered by naive height by in [2] and [3] respectively.

In 2018 he was awarded a Sloan Research Fellowship,[4] one of the most prestigious early career research fellowships available to mathematicians.[5]


  1. "Arul Shankar". Mathematics Genealogy Project. Retrieved 14 May 2017.
  2. M. Bhargava and A. Shankar, Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves, Annals of Mathematics 181 (2015), 191–242
  3. M. Bhargava and A. Shankar, Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0, Annals of Mathematics 181 (2015), 587–621
  4. "2018 Sloan Research Fellows". Alfred P. Sloan Foundation. Archived from the original on 1 November 2018. Retrieved 6 March 2018.
  5. "The Culture of Research and Scholarship in Mathematics: Rates of Publication" (PDF). American Mathematical Society. Retrieved 6 March 2018.

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