Abstract: Let R be a local ring. A finitely generated R-module M is said to be Ulrich if it is maximal Cohen-Macaulay and if its Hilbert-Samuel multiplicity is equal to its minimal number of generators. These modules have rich properties, and their existence has deep consequences for the base ring R. However, recent work of Yhee shows they need not exist in general, and the situations where they are known to exist are quite sparse. It is thus natural to look for weaker conditions which still retain some of the desired properties of Ulrich modules. In this talk, we will discuss several ways one can meaningfully relax the Ulrich condition. We will overview various properties enjoyed by these generalizations as well as some cases where existence can be established. This is based on joint work with Olgur Celikbas, Ryo Takahashi, and Yongwei Yao. Speaker(s): Justin Lyle (University of Arkansas)