Title: Effective verification of Tunnell's Criterion

Speaker: Nathan Ryan

Abstract: A classical problem is that of determining whether or not a given integer is the area of a triangle with rational sides. Such an integer is called congruent. In the early 1980s Tunnell gave an algorithm, assuming BSD, that determines if a number is congruent in O(n^3/2) steps. We will present two algorithms to verify Tunnell's criterion: one is randomized and of O(n^1/2) the other one deterministic of O(n^1/2) and storage O(n^o(1)).