Deligne Categories and Representation Theory in Complex Rank
Akhil Mathew
The summer after my junior year, I went to the Research Science Institute (RSI) program at MIT. I had a blast there, and I strongly encourage any eligible students reading this to apply. I had two mentors: a graduate student named Dustin Clausen and a professor named Pavel Etingof. My mentors contacted me before the program to tell me about a potential project on representation theory in complex rank, following a paper of Deligne that laid the groundwork and beginning work on a program that Etingof himself had proposed in a talk at the Newton Institute. There were a few obstacles. First, Deligne writes in French. It’s a good thing that I take the language in school, but I’m not terribly fluent. Fortunately, mathematicians tend not to use diffcult words; most of the technical math jargon consists of cognates anyway. Recognizing “categorie” as “category” does not require translator-level skills. A more serious diffculty was that Deligne’s paper is hard. Academic math papers in general have a tendency to focus on correctness over understandability (the word “trivial” is used very differently by research mathematicians and other people, for instance). Deligne’s paper also heavily uses the language of category theory, a branch of mathematics whose dryness has earned it the nickname “abstract nonsense” among mathematicians…
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