Algebraic representations and constructible sheaves

I survey what is known about simple modules for reductive algebraic groups. The emphasis is on characteristic p > 0 and Lusztig’s character formula. I explain ideas connecting representations and constructible sheaves (Finkelberg–Mirković conjecture) in the spirit of the Kazhdan–Lusztig conjecture. I also discuss a conjecture with S. Riche (a theorem for GL n ) which should eventually make computations more feasible.