Speaker: Xiannan Li

Abstract: I will describe two very classical Diophantine problems.  The first asks for understanding of right angle triangles with integer side lengths.  The second asks for right angle triangles with integer area and rational side length.  The solution to the first is relatively easy, while the second is connected to rational points on quadratic twists of elliptic curves and the order of vanishing of L-functions at the critical point.

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