Here are some topics I would be willing to supervise reading courses in.

Algebraic Cycles and Motives (roughly following Fulton/Manin)
Algebraic Stacks (roughly following Olsson/Stacks Project)
Higher Stacks (Lurie, Toen and others)
Classical groups and algebraic structures (following the Book of Involutions)
Tannakian Categories (following Milne/Deligne and some Lurie and others)