Congruent Number Problem and Heegner Points

Abstract

In this talk, the speaker will describe a method of Heegner to solve the equation y2 = x - x3 using modular parametrizations. In particular, Heegner showed that a prime p is a congruent number if it is 5 or 7 modulo 8. Such a work has been generalized by Stephen-Birch and Monsky to products of two primes.

About the speaker

Prof. Shou-Wu Zhang received his PhD from Columbia University in 1991. Before he joined Columbia University's faculty in 1996, he was a member of the Institute for Advanced Study in Princeton and an Assistant Professor at Princeton University. He rejoined Princeton University's faculty in 2011.

Prof. Zhang’s research areas include number theory and arithmetic algebraic geometry. He is on the editorial boards of the Journal of Algebraic Geometry, Journal of Differential Geometry, and Science in China, among other publications.

Prof. Zhang was an invited speaker of the International Congress of Mathematicians at Berlin in 1998 and was awarded a Morningside Gold Medal of Mathematics in the same year by the International Congress of Chinese Mathematicians for his work on the Bogomolov conjecture and Gross-Zagier formula. He was a Sloan Research Fellow, a Guggenheim Fellow, a L.-K. Hua Chair Professor at Chinese Academy of Sciences, a Changjiang Chair Professor at Tsinghua University, and a Prize Fellow at Clay Mathematical Institute. In 2011, he was elected Fellow of the American Academy of Arts and Sciences.