Triangles, Congruent numbers, and Elliptic Curves
Time and place
1:15 PM on Thursday, December 1st, 2016; NAC 4/148
Dr. Ruthi Hortsch (Bridge to Enter Advanced Mathemtics)
Abstract
We are all familiar with the Pythagorean Theorem, and perhaps with methods of constructing right triangles with all rational sides. While a right triangle with rational sides will always have rational area, does this work the other way round? For a given rational number n, can we find a right triangle with all sides rational that has area n? Not always---but this isn't obvious! If we can find such a triangle, we call the number n "congruent”. In the quest to discover which n are congruent, we will encounter elliptic curves and their group structure, and maybe even mention the elusive Birch and Swinnerton-Dyer Conjecture.
