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Abstract: Cumulant sequences are numerical sequences that play a fundamental role in noncommutative probability theory. West's stack-sorting map is a combinatorially-defined operator that acts on permutations. In this talk, we will discuss how cumulants and stack-sorting, two topics from very disparate worlds, are actually very closely related. This unexpected connection allows us to use tools from noncommutative probability theory to prove difficult, surprising, and (occasionally) weird facts about the stack-sorting map. We will explore several applications of this method.