Manjul Bhargava: What is the Birch-Swinnerton-Dyer Conjecture, and what is known about it?

Abstract:
The Birch and Swinnerton-Dyer Conjecture has become one of the central problems of number theory and represents an important next frontier. The purpose of this lecture is to explain the problem in elementary terms, and to describe the implications of Andrew Wiles' groundbreaking work to the problem. It will also summarize what is known to date towards the conjecture - including several recent advances - and, finally, what remains to be done!

Professor Manjul Bhargava is a Canadian-American mathematician. He is the R. Brandon Fradd 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.
Bhargava was awarded the Fields Medal in 2014. According to the International Mathematical Union citation, he was awarded the prize "for developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves".

This lecture was held at The University of Oslo, May 25, 2016 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations.

Program for the Abel Lecture 2016
1. "Fermat's Last Theorem: abelian and non-abelian approaches" by Abel Laureate Sir Andrew Wiles, University of Oxford
2. "Andrew Wiles' marvelous proof" by professor Henri Darmon, McGill University
3. "What is the Birch--Swinnerton-Dyer Conjecture, and what is known about it?" by professor Manjul Bhargava, Princeton University
4. "From Fermat's Last Theorem to Homer's Last Theorem" - a popular lecture by Simon Singh, author of Fermat's Last Theorem among other achievements. This lecture will never be published because the presentation contained material protected by intellectual property.

Видео Manjul Bhargava: What is the Birch-Swinnerton-Dyer Conjecture, and what is known about it? канала The Abel Prize