Time for another list of things I found interesting on the web the past 2 weeks.

  • Peter Krautzberger, Math on the web: time to step up! in which he announces the creation of a group of people interested in getting mathematics on the web. I'll keep you posted on its activities.

  • arXiv2BibTeX.org is a tool to quickly create Bib(La)TeX snippets for an arXiv entry, or a list thereof. The cool is thing that it also works for BibLaTeX, which happens to implement special support for the arXiv, automatically hyperlinking things. One not very crucial thing that is missing is the category (for the example there should be eprintclass = {math.CT}), but anyone can implement this and do a pull request.

  • Gonçalo Tabuada, Jacques Tits' motivic measure links the author's theory of noncommutative motives to the Grothendieck ring of varieties (also known as baby motives, or naive motives in the next preprint I'll link to), proving properties about the classes of Brauer–Severi varieties of central simple algebras in the latter from their properties as noncommutative motives. The codomain of the motivic measure is a ring that measures properties of all the possible subgroups the Brauer group of the base field, it being the quotient of the ring freely generated by all elements in the Brauer group modulo the relation that the sum of the unit and a product of two elements of coprime index is equal to their sum.

    There are more cool things you can do with noncommutative motives and Brauer–Severi varieties, about which I hope to blog soon.

  • Lieven Le Bruyn, Brauer-Severi motives and Donaldson-Thomas invariants of quantized 3-folds is also about the Grothendieck ring of varieties and Brauer–Severi schemes, but with the twist that it concerns Brauer–Severi schemes of orders. In February Brent Pym gave a very cool lecture in our departmental seminar about this preprint and it got Lieven interested in studying some of the conjectures in that preprint. He tackles the problem by using his awesome machinery of Cayley smooth orders, which happens to be the current topic of our student seminar, so maybe I'll blog a little about the details later on (if he doesn't already on his own blogs).

  • Daniel Chan, 2-hereditary algebras and almost Fano weighted surfaces discusses the generalisation of weighted projective lines in dimension 2. I've been thinking a little about this type of things lately, and I hope to blog about weighted projective lines and their deformation theory somewhere in the near future. For now, you'll have to do with this interesting preprint.