A \;graded algebr a A is Calabi-Yau of dimension n if the homologica l shift A[n] is a dualizing object in the appropri ate derived category. For example\, polynomial rin gs are Calabi-Yau algebras. Although many examples are known\, there are few if any \;classifica tion results. Bocklandt proved that connected grad ed Calabi-Yau algebras are of the form \;TV/(d w) where TV denotes the tensor algebra on a vector space V and (dw) is the ideal generated by the cy clic partial derivatives of an element w in TV. Ho wever\, it is not known exactly which w give rise to a Calabi-Yau algebra. We present a classificati on of those w for which \;TV/(dw) is Calabi-Ya u in two cases: \;when dim(V)=3 and w is in V^ {\\otimes 3} and when dim(V)=2 and w is in V^{\\ot imes 4}. \;We also describe the structure of& nbsp\;TV/(dw) \;in these two cases and show t hat (most) of them are deformation quantizations o f the polynomial ring on three variables. \; LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR