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The surface of cuboids and Siegel modular threefolds

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A perfect cuboid is a parallelepiped with rectangular faces all of whose edges, face diagonals and long diagonal have integer length. A question going back to Euler asks for the existence of a perfect cuboid. No perfect cuboid has been found, nor it is known that they do not exist. In this talk I will show that the space of cuboids is a divisor in a Siegel modular threefold, thus allowing to translate the existence of a perfect cuboid to the existence of special torsion structures in abelian surfaces defined over number fields.

This talk is part of the Number Theory Seminar series.

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