May 4
Math/Stats Colloquium: Anthony Várilly-Alvarado
Speaker: Anthony Várilly-Alvarado (Rice University)
Title: Perfect Cuboids and Magic Squares of Squares
Abstract: 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 there exists a perfect cuboid, or a 3 x 3 magic square whose entries are distinct squares. What do these problems have in common? Secretly, they are both problems about rational points on algebraic surfaces of general type. 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.
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