Alexander Engström: Algebras related to graph colouring and cohomology of Artin groups

Abstract: I will discuss ideals whose generators correspond to connected components of a certain size in a graph. Interesting facts about graph colouring and cohomology of Artin groups can be derived as algebraic properties of these ideals. Special cases of them have been intensely studied, with its origin in results by for example Conca and Fröberg. The focus of this talk is not to survey those special cases, but rather to look at the more general setting and what can be useful in relation to combinatorics and group theory. I will try to state open problems that are attainable and interesting in that direction, and in particular related to projective resolutions and Rees algebras.