• In The symmetries of Covid-19 the neverending author (I think by now his blog is one of the, if not the most long-running pure mathematics blogs) shows that the Covid-19 virus cannot have icosahedral symmetry, despite it often being depicted as having this in artist's impressions of the virus.

    It's great to see Lieven back to blogging, and I strongly suggest paying attention to his blog in case you're not already doing so.

  • Alex Kite, Ed Segal: Discriminants and semi-orthogonal decompositions discusses facts and conjectures about derived categories of (not necessarily proper) toric varieties. In particular, a Jordan–Hölder property holds, in spite of this failing for arbitrary smooth projective varieties. For a good overview of the state-of-the-art, this is a really interesting read.

  • Elana Kalashnikov: Mirror symmetry for GIT quotients and their subvarieties are lecture notes from 2 years ago, but I only saw them recently. They nicely explain the interaction between mirror symmetry for Fano varieties and geometric invariant theory. The emergence of quiver flag varieties, and quiver flag zero loci, in mirror symmetry is a really interesting interplay between various things I like to think about, and if you are halfway as excited about these as I am, you're in for a treat!