Naive homotopical techniques in algebraic geometry

I’ll present a framework for making simple but effective homotopical arguments in algebraic geometry. These methods apply only in certain fortunate situations, but when they do, they yield surprising (to me) facts about basic geometric objects. My goal is to share clear, concrete examples—proofs you can follow and take home. This is based on work with Hannah Larson, Jim Bryan, Balazs Elek, and Ben Church, and connects to ideas developed by many others.