A perfect cuboid is a box such that the distance between any two
corners is a positive integer. A magic square is a grid filled with
distinct positive integers whose rows, columns, and diagonals add up
to the same number. To date, we don't know if a perfect cuboid
exists, or if a 3 x 3 magic square whose entries are distinct squares
exists. What do these problems have in common? Secretly, they are
both problems about rational points on algebraic surfaces of general
type with mild singularities. I believe there is no such thing as a
perfect cuboid or a 3 x 3 magic square of squares, and I will try to
convince you that geometry suggests this is so.

2-2:30pm: talk for graduate
students

Webmaster University of Houston
---
Last modified: April 11 2016 - 18:14:43