A representation of the category of finite sets is a linear algebraic object, which roughly consists of a sequence of representations V_n of the symmetric group S_n related by transition maps.  These representations occur naturally in several places including in the study of Kazhdan-Lusztig polynomials of braid matroids, the homology of moduli spaces of curves, and representations of the Witt Lie algebra of polynomial vector fields. I will discuss examples and applications of these representations and their associated generating functions and symmetric functions.

Speaker’s website: https://ptoste.github.io/