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, their passage to the motivic Hall algebra, and then to the AR quiver via the stack correspondence. This motivic Hall algebra and the Hall geometry already have 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. Using the Hall correspondence and its fibers, we show how to recover the AR quiver and AR sequences for a Dynkin quiver.
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.
Update (27th June, 2026): This note has been revised with a result and posted to arXiv with the title Hall Geometry and Auslander-Reiten Quiver, available to read at https://arxiv.org/abs/2606.27362.
Update (27th June, 2026): This note has been revised with a result and posted to arXiv with the title Hall Geometry and Auslander-Reiten Quiver, available to read at https://arxiv.org/abs/2606.27362.
