Local-global principles for generalized Fermat equations via stacks

Classical Diophantine problems can often be rephrased in the language of stacks, which allows the use of a wider geometric toolbox for such problems. In this talk I will describe such a rephrasing for a certain family of generalized Fermat equations of genus less than 1, and report on ongoing work on studing the statistics of the failure of the integral Hasse principle in this family. This talk is based on joint work with Juanita Duque Rosero, Chris Keyes, Andrew Kobin, Manami Roy and Yidi Wang, and does not assume any prior knowledge about stacks.