- Bridgeland, Hall algebras and Donaldson–Thomas invariants is a very nice survey article on some recent developments in this exciting area
- Lecoutre–Sierra, A new family of Poisson algebras and their deformations adds a new family of Artin--Schelter regular algebras in arbitrary dimension to our list of examples. Already in dimension 4 this classification is not finished, but based on Brent Pym's work we at least know what they look like when we place ourselves at $k[x_0,x_1,x_2,x_3]$ and look around. He found a new type of algebra in his classification, and it is this algebra which is now generalised to all dimensions. So I guess we now have skew polynomial algebras, Sklyanin algebras, (variations on) graded Clifford algebras and these Pym--Lecoutre--Sierra algebras which work in all dimensions (and of course central extensions of smaller ones).
- Tabuada, Recent developments on noncommutative motives can be seen as an update on the progress in the last 2 years since the publication of his lecture notes on noncommutative motives. My fascination for these objects is clear if you've read some of my other mathematical blogposts, and this article is a nice starting point for some of the new applications of the theory.
- Madore, La forme élégante du plan projectif complexe is a long and detailed discussion of what can be said about the projective plane if you consider it over the real numbers, the complex numbers, the quaternions and even the octonions, and how this was looked at from a classical point of view involving Lie groups. If you read French it is an interesting read!