Nilpotent singularities in positive characteristic

This project is concerned with the geometry of nilpotent cones in Lie algebras of simple algebraic groups. Specifically, the goal will be to study (perhaps classify) certain singularities arising as intersections of (transverse) slices to nilpotent orbit closures in Lie algebras of simple algebraic groups, in the case where the ground field has positive characteristic. Similar questions can be asked for unipotent orbit closures in the groups themselves.