# Fortnightly links (169)

Henning Krause: Completions of triangulated categories are lecture notes on (you'd never guess) completions of triangulated categories. It's amazing how useful completion has turned out to be in this subject, and these lecture notes are an excellent introduction.

Shinnosuke Okawa: Semiorthogonal indecomposability of minimal irregular surfaces proves that (minimal) surfaces whose $\mathrm{H}^1(S,\mathcal{O}_S)$ is nonzero (= irregular) have an indecomposable derived category. This rules out any interesting semiorthogonal decompositions for surfaces of general type, except those for described explicitly in Corollary 1.10. I don't know examples of such surfaces. Do you? Please tell me!

Warren Cattani: On the derived category of IGr(3, 9) constructs a full exceptional collection (in fact a minimal Lefschetz collection) on the horospherical variety IGr(3, 9). Cool!

Geordie Williamson: Is deep learning a useful tool for the pure mathematician? gives both a gentle introduction to neural networks and deep learning, and an overview of how it has been successful already in pure mathematics. The question that I'm wondering about is: when is the first big result in algebraic geometry coming from these methods? Or have I missed something already?