20240528 Raymond Cheng

Which are the simplest hypersurfaces in projective space? Traditionally, these are those defined by low-degree polynomial equations: quadrics, cubics, quartics, and so forth. Over fields of positive characteristic, however, the shape of the defining equation also plays a dramatic role. The aim in this talk is to explain a circle of ideas that identifies a class of hypersurfaces in positive characteristic that, due to the special shape of their defining equations, are much simpler than they first seem. I will intimate a philosophy for understanding them, formulate a few precise results, and pose some questions I would like resolved.