Nilpotent orbits and quiver representation theory

This project explores new connections between quiver representation theory (QRT) and Lie theory (LT) with potential applications to quantum theory (QT). The connection between QRT and LT dates back to the famous Gabriel-Kac Theorem on root systems and quiver representations and have since drawn enormous attention and effort into the area. It led to a substantial contribution of QRT to QT, via a sequence of work by Ringel (Bielefeld, Germany), Lusztig (MIT, USA) and Nakajima (Kyoto, Janpan). Jensen, Su and Yu's recent work on open orbits in biparabolic algebras/seaweeds strengthens the connection and opens up a new research field, which the proposed project is to study.

In the first year of his study, he will learn the basic courses related to the project, quiver representation theory, homological algebra and affine Lie algebras. Later in the year, he should also move on to more specific topics on Richardson elements/generic orbits in Lie algebras and quiver representations, and aim for a good understanding of the main results on the subject in the literature. He will start to do some computation and explore the possible new connections between the subjects.