Manjul Bhargava in 2014
Manjul Bhargava in 2014
Four Fields medallists left to right (Artur Avila, Martin Hairer (at back), Maryam Mirzakhani, with Maryam's daughter Anahita) and Bhargava at the ICM 2014 in Seoul

Bhargava and Shankar's unconditional proof of the boundedness of the average rank of elliptic curves is obtained by using a certain exact sequence involving the Mordell-Weil group of an elliptic curve, then one would be able to bound the Mordell-Weil rank on average as well.

- Rank of an elliptic curve

Proof (with Arul Shankar) that the average rank of all elliptic curves over Q (when ordered by height) is bounded.

- Manjul Bhargava
Manjul Bhargava in 2014

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