Spring 2014, Thursdays, Blocker 113, 4:00-4:50 PM

Date: March 27

"  The congruent number problem "
  Detchat Samart  


A positive rational number $r$ is called a congruent number if it is the area of a right triangle all of whose sides are rational. The congruent number problem asks if there is an algorithm for checking in a finite number of steps if a given positive integer $N$ is congruent or not. The problem has a very long history, yet remains unsolved in general. In 1983, Tunnell used the modern theory of elliptic curves and modular forms to show that the problem can be solved completely if the BSD conjecture is true. In this talk, we will briefly explain what elliptic curves and modular forms are and how they come into play in the attempt to resolve the problem.