• Victoria Hoskins: Moduli spaces and geometric invariant theory: old and new perspectives is a great survey paper on constructions of moduli spaces in algebraic geometry. Highly recommended reading!

  • Andreas Hochenegger, Andreas Krug: Asymmetry of $\mathbb{P}$-functors answers a question of Anno and Logvinenko on adjoints of $\mathbb{P}$-functors necessarily being $\mathbb{P}$-functors. Spoiler: the answer is no. The paper is a nifty short argument, and fun to read!

    What is the plural of Andreas? Andreae?

  • Mátyás Domokos: Quiver moduli spaces of a given dimension shows a really cool result in my opinion. Namely that there are only finitely many quiver moduli spaces of a certain dimension. A priori there are only countably many (as the set of quivers, dimension vectors, and chambers in the stability space is countable) but under certain assumptions, it is shown that there are in fact only finitely many.

    Thus it is also an interesting question to be able to write down the list of these. In the spirit of Totaro's question about Bott vanishing for Fano varieties I'd be particularly interested in the Fano case. There is by the way no obvious link between Bott vanishing and Fano quiver moduli: Grassmannians are Fano quiver moduli but fail Bott vanishing, and e.g. 2–36 is not a Fano quiver moduli space as per the last line of Fano quiver moduli.

    This is closely related to some things I've been thinking about recently, and I hope to be able to share the results soon. Stay tuned!