PIMS-SFU Colloquium: Anthony Varilly-Alvarado

The talk is aimed at a general academic mathematical audience, so should be suitable for graduate students, post-docs, and faculty.

The set of solutions to a diophantine equation is strongly influenced by the geometry of the associated algebraic variety. This paradigm, for example, suggests that an elementary proof of Fermat’s Last Theorem is unlikely to exist. I will describe what the paradigm suggests about diophantine equations whose geometric avatars are surfaces. In particular, I will introduce the Grothendieck-Brauer group of an algebraic variety and show how it explains the shape of the set of solutions to certain diophantine equations.