This is an attempt for me to have working knowledge of Hochschild cohomology. In their paper "Some extensions of theorems of Knörrer and Herzog–Popescu", Alex Dugas and Graham Leuschke are constructing an endomorphism ring which behaves like a hypersurface ring in that every module has a resolution which eventually becomes 2-periodic. We would like to compute the Hochschild cohomology as more evidence towards the open question/philosophy that noncommutative algebras with Noetherian Hochschild cohomology might make good noncommutative complete intersections. If things turn out okay, the Hochschild cohomology of the endomorphism algebra of Dugas and Leuschke should have Krull dimension one.