I am specifically interested in studying Hopf actions on path algebras of quivers, an area that lies at the intersection of algebra, geometry, and representation theory. Path algebras are algebraic structures associated with quivers , and the actions of Hopf algebras introduce symmetry and quantum symmetry into these systems.

I am specific interesred lies on understanding when bosonization gives rise to a Hopf algebra and how these resulting Hopf algebras act on the path algebras of quivers. I am particularly interested in classifying these actions, exploring patterns, and potentially generalizing them across different types of bosonizations. My work builds upon foundational studies in this field, including the classification of Hopf actions by Kinser and Oswald.