Arul Shankar is an Indian mathematician at the University of Toronto specializing in number theory, particularly arithmetic statistics.
He received his B.Sc. (honours) in mathematics and computer science from Chennai Mathematical Institute in 2007. He obtained his PhD from Princeton University in 2012 under Manjul Bhargava. [1] 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 [2] and [3] 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, [4] one of the most prestigious early career research fellowships available to mathematicians. [5]
In mathematics, the Birch and Swinnerton-Dyer conjecture describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. It is named after mathematicians Bryan John Birch and Peter Swinnerton-Dyer, who developed the conjecture during the first half of the 1960s with the help of machine computation. As of 2024, only special cases of the conjecture have been proven.
In mathematics, the Sato–Tate conjecture is a statistical statement about the family of elliptic curves Ep obtained from an elliptic curve E over the rational numbers by reduction modulo almost all prime numbers p. Mikio Sato and John Tate independently posed the conjecture around 1960.
Manjul Bhargava is a Canadian-American mathematician. He is the Brandon Fradd, Class of 1983, Professor of Mathematics at Princeton University, the Stieltjes Professor of Number Theory at Leiden University, and also holds Adjunct Professorships at the Tata Institute of Fundamental Research, the Indian Institute of Technology Bombay, and the University of Hyderabad. He is known primarily for his contributions to number theory.
In mathematics, specifically the area of algebraic number theory, a cubic field is an algebraic number field of degree three.
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Lawrence Clinton Washington is an American mathematician at the University of Maryland who specializes in number theory.
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