The focus of this talk is to introduce and motivate the ring of Witt vectors (which is actually a ring-valued functor). With a heavy focus on examples, we will work through the construction of the Witt functor and describe the properties it satisfies, then spend the remainder of the talk describing reasons why one would want such a thing, and list applications in a variety of fields (including both varieties and fields) Speaker(s): Andy Gordon (University of Michigan)