Abstract

Recall that a positive integer is called a congruent number if it is the area of a right triangle with rational side-lengths.  The congruent number problem is to determine whether a given integer is congruent or not.  For example, Fermat showed that none of 1, 2, 3  is congruent, and Fibonacci showed that 5, 6, 7 are all congruent numbers.  In this talk, we introduce the background of this problem and recent progress.

About the speaker

Ye TIAN is a professor of mathematics in the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He is a leading researcher in number theory and an expert on the arithmetic of elliptic curves, with works published on top mathematical journals including Annals of Mathematics and Inventiones Mathematicae.  Due to his outstanding academic contribution, he was awarded the Morningside Silver Medal (by ICCM in 2007), the Morningside Gold Medal (by ICCM in 2013), and the Ramanujan Prize (by ICTP & IMU in 2013).  He had also been a Distinguished Young Scholar sponsored by NSFC and a Changjiang Scholar sponsored by the Ministry of Education.