In their 2021 paper, Fargues-Scholze formulated a remarkable conjecture giving a categorical upgrade of the local Langlands correspondence. This conjecture has striking consequences for the cohomology of local Shimura varieties, and is strongly analogous with the classical geometric Langlands conjecture. In the first talk, I will recall some of the background needed to precisely state the conjecture, and explain some of its consequences and significance. In the second talk, I will formulate a program to prove this conjecture for many groups. In particular, for the group GLn, I will explain how to reduce it to two much more approachable statements. This is joint work in progress with Lucas Mann.