Arul Shankar

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Arul Shankar is an Indian mathematician at the University of Toronto specializing in number theory, particularly arithmetic statistics.

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Education

He received his B.Sc. (honours) in mathematics and computer science from the Chennai Mathematical Institute in 2007. During his undergraduate studies, he was awarded the CMI Medal of Excellence in Mathematics for outstanding academic performance at the institute’s first convocation as a deemed university. [1] Through CMI’s exchange programme with the École Normale Supérieure, Paris, he undertook an eight-week summer research visit at ENS in May–June 2007. [1]

He obtained his PhD from Princeton University in 2012 under Manjul Bhargava. [2] Shankar is known for his work, with Bhargava, establishing unconditionally that the average rank of elliptic curves is bounded when ordered by naive height by [3] and [4] respectively, thus proving the Birch and Swinnerton-Dyer conjecture for a positive proportion of elliptic curves.

In 2018 he was awarded a Sloan Research Fellowship, [5] one of the most prestigious early career research fellowships available to mathematicians. [6] He was named a Simons Fellow in Mathematics in 2024, a fellowship awarded by the Simons Foundation to support research leave for established mathematicians. [7]

References

  1. 1 2 "CMI Annual Report 2007–2008" (PDF). Chennai Mathematical Institute. Retrieved 25 January 2026.
  2. ↑ "Arul Shankar". Mathematics Genealogy Project. Retrieved 14 May 2017.
  3. ↑ 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. https://dx.doi.org/10.4007/annals.2015.181.1.3
  4. ↑ 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. https://dx.doi.org/10.4007/annals.2015.181.2.4
  5. ↑ "2018 Sloan Research Fellows". Alfred P. Sloan Foundation. Archived from the original on 1 November 2018. Retrieved 6 March 2018.
  6. ↑ "The Culture of Research and Scholarship in Mathematics: Rates of Publication" (PDF). American Mathematical Society. Retrieved 6 March 2018.
  7. ↑ "2024 Simons Fellows in Mathematics Announced". Simons Foundation. 20 March 2024. Retrieved 25 January 2026.


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