摘 要: I will discuss several topics of modular representation theory of restricted Lie algebras. This will include the following topics: 1. reduced enveloping algebras and the current state of the first Kac-Weisfeiler conjecture;
????2. nilpotent orbits and sheets in reductive Lie algebras;
????3. support varieties for non-restricted modules and the second Kac-Weisfeiler conjecture;
????4. finite W-algebras and their modular analogues;
????5. small modular representations and multiplicity-free primitive ideals;
????6. some open problems.