Fortnightly links (11)

Goncalo Tabuada, A note on Grothendieck's (noncommutative) standard conjecture of type D: I have blogged before about noncommutative motives and Grothendieck's conjectures, and this preprint discusses how the (commutative) conjecture D follows from the noncommutative version of conjecture D, which can be proven certain classes of objects whose derived categories are wellunderstood. Cool!

Alexander Kuznetsov and Alexander Perry, Derived categories of Gushel–Mukai varieties is a cool preprint about a class of varieties whose birational geometry (and derived categories) are closely related to those of cubic fourfolds, about which I blogged earlier: as for a cubic fourfold it is expected that a generic one is not rational, which should be reflected on the level of derived categories. What is so funny about Gushel–Mukai varieties is that they are the intersection of a Grassmannian, a projective space and a quadric hypersurface, which makes them very amenable to the tools available for derived categories of varieties.

John D. Cook, The acoustics of kettledrums explains the mathematics behind the fundamental and overtones for a kettledrum, and how an actual kettledrum (also known as tympani) needs to be not quite a theoretical kettledrum, otherwise it wouldn't be useful as an instrument!

Remy van Dobben de Bruyn, Odd degree Betti numbers are even is yet another interesting blogpost by my former classmate Remy, about computing the odd Betti numbers for proper nonprojective smooth varieties over a finite field and showing that they are always even.

President Obama gives Michael Artin a medal for his contributions to noncommutative algebraic geometry is precisely what it says. Hurray for Artin and noncommutative algebraic geometry in general! Lately I've been reading lots of Artin's work on the structure of orders, and it is always a treat to read.