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Abstract: Cofibrant modules, as defined by Benson, play important roles in many cohomology questions of infinite discrete groups. In this talk, I will (a) talk about my new work on the relation between the class of these modules and Gorenstein projectives where I'll build on Dembegioti-Talelli's work, and (b) highlight new results from one of my older papers on the behaviour of an invariant closely related to these modules. If time permits, I'll show a possible generalization of many of these results to certain classes of topological groups.