# Dimer quivers on genus g surfaces and noncommutative desingularizations

A dimer algebra is a type of Jacobian algebra whose quiver $$Q$$ embeds in a surface $$S$$, such that each connected component of $$S\backslash Q$$ is simply connected and bounded by an oriented cycle of $$Q$$. It was shown in 2009 that noetherian dimer algebras on a torus are noncommutative desingularizations of their centers; in particular, they are ‘homologically smooth’ endomorphism rings. On higher genus surfaces, however, these nice properties disappear. I will introduce special quotients of dimer algebras, called ‘ghor algebras’, where the relations come from the quiver’s perfect matchings rather than a potential. On a torus, a dimer algebra coincides with its ghor algebra if and only if it is noetherian, whereas ghor algebras are almost never noetherian on higher genus surfaces. Nevertheless, I will describe how a ghor algebra, on any genus $$g$$ surface, may be viewed as a noncommutative desingularization of its center. This is joint work with Karin Baur.