Thuses is a new online math platform, aimed at being a central hub for what otherwise would be interesting mathematical blogposts scattered all over personal blogs. But I guess the big takeaway is that most of the contributors would not start a personal blog, or if they did, they would never get the exposure they could now. Head over there for great content!
Henning Krause: Homological theory of representations is the (finished) draft of a book to be published soon, about the representation theory of associative algebras from a homological / categorical point of view. It's a great read, taking an abstract but not too abstract approach to things.
Alexander Kuznetsov: Categorical absorption of singularities and nodal nonfactorial Fano threefolds is the video of a talk by Sasha, giving a preview of work-to-come with Evgeny Shinder. The streaming seems to be suboptimal because of the file size, so downloading it is maybe advised.
Ed Segal: Mirrors to surfaces and twisted derived categories is another video, giving a preview of work of just Ed himself. What I liked so much about this talk is that it's the first instance of the derived Brauer group making an appearance in something "down-to-earth", namely what is the mirror to a certain punctured surface? Cool stuff!
This also serves as a reminder that the Derived seminar is a great event.