Title: Recent results about tilting modules for algebraic groups
Abstract: We will survey the theory of tilting modules for a reductive algebraic group G in positive characteristic, including their role in a new approach toward a character formula for simple G-modules. We will discuss the significance of a longstanding conjecture by Donkin about the indecomposability of certain tilting modules over the Frobenius kernel of G, and look at the current status of this conjecture.