K-polynomials of type A quiver orbit closures and lacing diagrams

This article contains an overview of the author's joint work with Allen Knutson and Jenna Rajchgot on $K$-polynomials of orbit closures for type $A$ quivers. It is written to an audience interested in interactions between representations of algebras, algebraic geometry, and commutative algebra. A few open problems resulting from the work are also explained.