Stephen Morgan

Mathematical Sciences Institute
The Australian National University

I am currently a research fellow at the Mathematical Sciences Institute of the Australian National University. Before that, I was a research member at the Mathematical Sciences Research Institute in Berkeley, California during the Fall semester of 2014. I study geometric representation theory and W-algebras, and completed my PhD at the University of Toronto under Joel Kamnitzer. Before that, I received my undergraduate degree in mathematical physics from Queen's University.

Research interests

My research lies in the general areas of geometric representation theory and categorification, both fields which attempt to better understand problems in classical representation theory through the introduction of geometric intuition or higher structure. More specifically I study W-algebras, objects which are closely tied to both the Lie theoretic and Poisson geometric worlds.

The representation theory of W-algebras is strongly related to the classical study of the BGG category O, an object of interest in Lie theory. In particular, a given infinitessimal block of category O can be shown to be equivalent to a subcategory – analogous to category O – of the modules for a particular W-algebra. With this relationship, we can begin to look at many classical categorification constructions using category O from the point of view of W-algebras, gaining new insight into their workings.

For more detailed information, please refer to my statement of research interests (A4) and my curriculum vitæ (A4).