Magnus Carlsson: The étale homotopy type and Diophantine equations

In 2010 Harpaz-Schlank showed that one can understand the Brauer-Manin obstruction and other obstruction theories for diophantine equations in a conceptual, unified way, through certain homotopy obstructions. We will in this talk give a brief introduction to these ideas, sketch how to calculate these obstructions and pose some open questions and how they might be resolved.