• Periods in Number Theory, Algebraic Geometry and Physics is the blog for the Hausdorff Institute trimester. I really like this initiative.

• Alexander Kuznetsov, On linear sections of the spinor tenfold, I is an interesting preprint for many reasons: if you like homological projective duality, it studies a homologically projectively self-dual variety; if you like partial flag varieties, it gives many viewpoints on the spinor tenfold; and if you like minifolds, it gives a new family of 5-dimensional minifolds! Recall that a minifold is a smooth projective variety $X$ such that $\mathbf{D}^{\mathrm{b}}(X)$ has a full and strong exceptional collection of length $\operatorname{dim}X+1$. Examples are projective spaces and odd-dimensional quadrics, and in dimension 3 there exists a complete classification. In dimension 5 this preprint makes me wonder whether there are 5-dimensional minifolds of index 4, 2 and 1 (as we have examples of index 6, 5 and 3). In dimension 3 there are 4 possible indices, and they are all obtained.

• Adeel Khan, Descent in algebraic K-theory is the course website for a course on the algebraic K-theory of derived schemes. Recently derived algebraic geometry has been used to prove Weibel's conjecture on the vanishing of negative algebraic K-theory of finite-dimensional noetherian schemes below minus the dimension, and the course aims to discuss the proof by Kerz–Strunk–Tamme.