New Age Linkage

The linkage principle says that the category of representations of a reductive group GG in positive characteristic decomposes into "blocks" controlled by the affine Weyl group. We will discuss the beautiful geometric proof of this result that Simon Riche and Geordie Williamson obtained by applying Smith-Treumann theory to the Iwahori-Whittaker model of the Satake category... and, as a bonus, a tilting character formula valid for all dominant weights and all characteristics!