- Yujiro Kawamata, Derived McKay correspondence for $\mathrm{GL}(3,\mathbb{C})$ is the generalisation of the famous Bridgeland–King–Reid McKay correspondence for $\mathrm{SL}(3,\mathbb{C})$. In this case it is not just an equivalence of the derived category of the quotient stack with the derived category of a crepant resolution, because the elements of the finite subgroup $G\subset\mathrm{GL}(3,\mathbb{C})$ not contained in $\mathrm{SL}(3,\mathbb{C})$ will contribute (relative) exceptional objects, which are described explicitly and which depend in a complicated way on the subspaces of $\mathbb{C}^3$ fixed by those elements. Cool!
- Arnaud Beauville, An introduction to Ulrich bundles is precisely what I wanted to write, but of course infinitely better. I have come across Ulrich bundles a few times now, but only in the titles of talks that I didn't attend or papers I haven't read, hence I planned on doing an outsider's attempt at a What is... column on Ulrich bundles to figure out what was going on, but I will now refer you to his overview paper. One thing I would still like to figure out is the role of Ulrich bundles in the context of derived categories, besides the possible coincidence that indecomposable Ulrich bundles on a quadric are related to spinor bundles.
- From time to time I am confronted with the awesomeness of finite group theory, and this time it's by GroupNames which gives an overview of the structure of finite groups of sufficiently small order, explaining how various classes are defined and what the properties of its members are. I remember piecing together this kind of information from GAP's
StructureDescription and CharacterTable functionality, but this is much easier and much prettier.