Abstract: In these talks, I will recall the categorical local Langlands conjecture of Fargues-Scholze, and explain a strategy of proof for many groups, in particular for GL_n. In the first talk I will recall some of the geometry and basic setup, and give a precise statement of the conjecture. In the second talk I will state our results and give an outline of the proof strategy and new ideas. The final talk will be an informal Q&A/office hours discussion with some example calculations and arithmetic applications to the cohomology of local and global Shimura varieties. This is all joint work with Lucas Mann, and relies on other joint works in progress which I will mention during the talks.