# Fortnightly links (44)

Dmitri Kaledin, Witt vectors, commutative and noncommutative is a pretty preprint on (you'd never guess) Witt vectors. Its introduction is a really nice overview of the history of the subject, and explains in a nice way the interesting role that Witt vectors play in mathematics. The goal of the preprint is to describe Hochschild–Witt homology and discuss some of its (conjectured) properties.

Daniel Halpern-Leistner, The D-equivalence conjecture for moduli spaces of sheaves is a note explaining a proof of the Bondal–Orlov conjecture in high dimension for a specific type of Calabi–Yau manifolds, namely those which are birational to a moduli space of (Gieseker semistable) coherent sheaves on a K3 surface. Recall that they conjectured that projective birational Calabi–Yau's are automatically derived equivalent, a result which is known in dimension 3. So if your favourite Calabi–Yau varieties look like the $\mathop{\rm Hilb}^n X$ of a K3 surface $X$, you can now apply wall-crossing and get your desired derived equivalences!

Finally, Pavel Etingof, A counterexample to the Poincaré–Birkhoff–Witt theorem is a slightly provocative abstract for a talk, but he quickly explains how it's not a counterexample to the PBW as you know it, but an analogue for general symmetric tensor categories, and in this case it fails for the Verlinde category.