In this talk, I will discuss the classifying space for the family of virtually cyclic subgroups. In particular, I will introduce an interesting conjecture due to Juan-Pineda and Leary. The conjecture says a group admits a finite model for the classifying space for the family of virtually cyclic subgroups if it is virtually cyclic. I will talk about some recent progress on this conjecture. This is a joint work with Tim von Puttkamer.

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