A constructible realization of modules over the rational Cherednik algebra in characteristic p

I will talk about work in progress aiming to establish a constructible realization of the derived category of modules over the rational Cherednik algebra in positive characteristic. Tools for doing this include the Drinfeld-Laumon construction from the geometric Langlands program, categorification of the elliptic Hall algebra, and combinatorics of the Mullineux involution for modular representations of the symmetric group. Parts of this project are joint with Roman Bezrukavnikov and Guangyi Yue.