• Hans Franzen: A Gelfand-MacPherson correspondence for quiver moduli provides a sweeping generalisation of the fact that there exists an isomorphism of varieties $\operatorname{Gr}(k,n)//\mathbb{G}_{\mathrm{m}}^n\cong(\mathbb{P}^{k-1})^n//\operatorname{SL}_k$ (depending on some choice of stability condition). It says that a moduli space of quiver representations can be written in two ways as the quotient of a certain quiver Grassmannian. Cool!

• Adam Topaz: Algebraic dependence and Milnor K-theory proves that Milnor K-theory fully determines a field (in many situations). I'd love to have a discussion about how this is (not) surprising, for an absolute non-expert it in any case sounds like a wonderful statement.

• Laurent Manivel: A four-dimensional cousin of the Segre cubic talks about generalising the Segre cubic to other (higher-dimensional) settings, and focuses on a 4-dimensional case. Don't forget to read Section 9 for some glimpse into the higher-dimensional cases.