symmetric functions are highly ubiquitous in algebraic combinatorics, with connections to the representation theory of $gl_n$ and $s_n$, the geometry of grassmannians, and more. there is a classical way to 'compose' symmetric functions called plethysm which has a nice representation-theoretic interpretation. we will describe a related operation called chern plethysm which has inputs given by a symmetric function f and a vector bundle e and outputs a symmetric polynomial. chern plethysm provides numerous schur-positivity results, indicating a representation-theoretic connection, but finding this connection remains an open problem. joint with sara billey and vasu tewari.