• Alice Rizzardo and Michel Van den Bergh: A $k$-linear triangulated category without a model gives an example of (drumroll...) a $k$-linear triangulated category without a model, i.e. without an enhancement (as a dg category, or equivalently an $\mathrm{A}_\infty$-category), where $k$ is a field.

It nicely complements the earlier (and much easier) preprint A note on non-unique enhancements by the same authors, where an example of $k$-linear triangulated category is given with two enhancements.

Are there more possible pathologies of triangulated categories, linear over a field, that aren't resolved yet?

• Remy van Dobben de Bruyn's preprints and drafts are available on his personal webpage. If you like your algebraic geometry to be done over fields of positive characteristic, then you're in for a treat, with some really nice results.

• Tutorial: visualizing root systems is a tutorial for (drumroll...) visualising root systems in Sage. It is really useful that you can draw these things to get a feel for what the computations in a root system look like, and the results look stunning.