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

## TL;DR

This paper reviews joint work on K-polynomials of orbit closures in type A quivers, highlighting connections between algebraic geometry, representation theory, and commutative algebra, and discusses open problems in the area.

## Contribution

It provides an overview of new results on K-polynomials of type A quiver orbit closures and their relation to lacing diagrams, with insights into open problems.

## Key findings

- K-polynomials of type A quiver orbit closures characterized
- Connections established between algebraic geometry and representation theory
- Open problems proposed for further research

## Abstract

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.