McMaster University, December 5 - 8, 2014
The box variety is an explicit algebraic surface in 6-dimensional projective space whose points with positive integer coordinates correspond precisely to the perfect cuboids. In the last few years several people (Beauville, Freitag, Salvati Manni, Stoll, Testa and others) have studied the geometric structure of the box variety, and this sheds new insight into the above open problems.
In my talk I will first discuss some early history of perfect cuboids. Then I will explain what is known about the box variety, and how this relates to the open problems.
Followin Murty and Wong, we investigate the largest prime divisor of the terms in an Elliptic Divisibility Sequence.
This is joint work with Amir Akbary.