Seminars on Congruent Number Problem
Abstracts
Congruent Number Problem and Elliptic Curves (5 July 2012)
In this talk, the speaker will first discuss the relation between the congruent number problem and elliptic curves y2 = x3 - x. A solution assuming the BSD conjecture will be described.
Congruent Number Problem and Heegner Points (10 July 2012)
In this talk, the speaker will describe a method of Heegner to solve the equation y2 = x3 - x 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.
Work of Tian Ye (12 July 2012)
In this talk, the speaker will describe recent work of Prof. Tian Ye (Morningside Center of Mathematics, Chinese Academy Sciences) who produced a large class of congruent numbers with arbitrary many prime factors.
About the speaker
Prof. Zhang Shou-Wu received his PhD from Columbia University in 1991. He was a member of the Institute for Advanced Study in Princeton and an Assistant Professor at Princeton University from 1991 to 1996. He has been tenured at Columbia University since 1996 and at Princeton University since 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.
