This month's post is rather about an announcement of a note that I have written titled "Quiver Moduli, Motivic Hall Algebra, and Auslander-Reiten Triangles", which is available at this link. The note discusses quiver moduli and their passage to the motivic Hall algebra. This motivic Hall algebra already has data on extensions, which can provide a playground for AR theory in both abelian categories ($\text{Rep}_{k}Q$ or $\text{Mod-}kQ$) and the derived category/triangulated settings. But we use Happel's theorem to pass to another equivalent category of stable modules over the repetitive algebra of $kQ$, the path algebra of finite global dimension—for an exposition about Happel's theorem, you may read this talk.
Obviously, AR theory is a specific interest, which can lead to other general themes in homological algebra. Moreover, this passage has interesting potential points about the algebra of BPS states.
