Fortnightly links (26)
With a delay of one day due to Christmas related festivities, here is a list of interesting reading for the holidays.
Goncalo Tabuada and Michel Van den Bergh: Additive invariants of orbifolds is a really interesting paper if you care about derived categories, and algebraic stacks. It continues the two authors' work on additive invariants, and reading the introduction gives you a nice overview of the results. One thing in particular that I really liked is remark 1.22, where an additive decomposition of the Kummer K3 surface is given, which does not come from a semi-orthogonal decomposition of the derived category (because it is indecomposable).
Alexander Kuznetsov and Evgeny Shinder, Grothendieck ring of varieties, D- and L-equivalence, and families of quadrics is another paper for which I strongly suggest reading the introduction. It gives a pretty overview of the relationship between the Grothendieck ring of varieties (also known as Grothendieck's baby motives) and derived categories of smooth projective varieties, and formulates some precise conjectures.
Helmut Lenzing, Weighted projective lines and Riemann surfaces is an overview paper on weighted projective lines by the mathematician who actually introduced them in the 1980s. It came at a perfect time for me (but I missed it when it appeared, hat tip to Theo Raedschelders for mentioning it), as I gave a lecture on these objects in our graduate student seminar, as they are important objects that connect the theory of algebraic stacks, derived categories and tilting theory, representation theory of algebras and hereditary orders on curves. Maybe I'll write a bit more later about them on my blog, discussing some specific examples.
Kevin De Laet, On the center of 3-dimensional and 4-dimensional Sklyanin algebras applies the author's method of equipping the pieces of a graded algebra (as they appear in Artin–Zhang style noncommutative algebraic geometry) to describe some well-known (computational) facts about Sklyanin algebras regarding their centers for which a conceptual explication was lacking. Nifty!
I'm not sure what happened, as I'm sure that TeX talk existed before, and that their interviews where previously featured on the TeX Stack Exchange blog, but suddenly new posts started appearing in my news feed so maybe they reconfigured something or other. In any case, it's good to see high quality LaTeX blogs, be sure to add this to your feeds.
Gaëtan Hadjeres and François Pachet, DeepBach: a Steerable Model for Bach chorales generation is an impressive example of what artificial intelligence can do in music composition. I am very much into counterpoint and fugues, which are very rigid rule-based methods of composition. Chorales are more homophonic, which makes them more viable to machine learning methods, but it is still an impressive accomplishment that a computer can do such a good job by just observing the examples of Bach without actually telling them about the rules from four-part harmony. Be sure to check out the audio of their examples!