swMath is "an information service for mathematical software", basically a search engine for such software. By telling you about it, I can hopefully remember to take a look whenever I need to compute something. It also has mathematical databases, maybe I can find an interesting data set in there and provide it with a pretty(-ish) web interface if I need any more distractions!
Manjul Bhargava, Bjorn Poonen: The local-global principle for integral points on stacky curves concerns the Hasse--Minkowski theorem, and shows that for stacky curves of Euler characteristic at least 1 the local-to-global principle holds, while it can fail for Euler characteristic 1 and below.
Bernhard Keller: Singular Hochschild cohomology via the singularity category concerns a naive question I asked Zhengfang Wang back in 2015 on a walk through Kongens Have in Copenhagen: is the notion of singular Hochschild cohomology of an algebra that Zhengfang introduced in his PhD thesis (defined as the shifted endomorphisms of an algebra in the singularity category of its enveloping algebra) the Hochschild cohomology of a dg category (preferably the singularity category of the algebra itself)?
I'm now linking the second version of Bernhard's preprint, where the first version showed that the answer was yes, and the current one shows that the answer in general can be no (but is often yes). The problem can be paraphrased as the distinction between smoothness (which is a relative notion) and regularity (which is absolute), and that these can differ, even for finite-dimensional algebras over a field.