• Ever wondering what a good notation for some finite group is? Or how to give a succinct description of it? Or just see a wealth of other group-theoretic information for finite groups of order at most 500? One can use groupnames.org for this.

    I couldn't find information about how the system is set up unfortunately. It'd be interesting to learn more about that.

  • Daniel Huybrechts: Hodge theory of cubic fourfolds, their Fano varieties, and associated K3 categories discusses the Hodge and lattice-theoretic properties of cubic fourfolds. In all honesty, this is an aspect that I know very little about, but these notes definitely make the literature less daunting.

  • Adeel Khan: Descent by quasi-smooth blow-ups in algebraic K-theory proves Orlov's blowup formula in the very general setting of perfect complexes on a derived Artin stack with quasi-smooth centre. I'm wondering whether the statement now is sharp, or whether there are even more general cases in which a blowup formula must hold. Also a new criterion for cdh descent is given, and this is used to give a clean proof that homotopy invariant K-theory satisfies it.