I'm currently putting together an application for a dissertation completion fellowship offered through my university. A part of the application includes 500-1000 words describing my dissertation. The prompt for this description includes the following:
The proposal should make a compelling statement about the planned work and be accessible to scholars in a broad range of fields.
My research and dissertation topics are representation theory and cohomology of algebraic groups, affine group schemes, and (restricted) lie algebras over fields of positive charactersitic. How can I describe these topics in such a way that is "accessible to scholars in a broad range of fields?"
I will be competing against PhD students from various departments, and I feel that the esoteric nature of research level mathematics has me at an inherent disadvantage in applying for this fellowship.
I'm looking for suggestions about how to write about modular representation theory and cohomology in a compelling and accessible way. I imagine discussing applications to other academic disciplines would be one way to do this, so it would also be helpful to know applications in other fields (physics is an obvious one that comes to mind).
Thanks in advance for any suggestions.