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I am PhD student in plant biology at the University of Georgia, Savannah River Ecology Lab. The mathematics I do is part hobby and part work. I don't have much formal training (in terms of courses), but I have self-studied quite a bit (undoubtedly there are plenty of gaps in my knowledge).
I primarily got interested in category theory through John Baez' papers (and some attempts at programming in Haskell). I saw John's paper Relative entropy in biological systems linked on the /r/math subreddit of reddit. I really liked that paper because it used some interesting math to change the way I conceive of evolution and ecology. From that paper, I was led to papers on using category theory to analyze/formalize diagrams in science (e.g., A compositional framework of passive linear networks). So I started to think I might be able to find applications of category theory to the systems I already study for work.
I think compositionality will be a useful idea in studying complex biological systems, especially ones where it is difficult to measure or control phenomena of interest. By describing how systems (e.g., plant tissues) composed to form bigger systems (e.g., whole plants), we can then deduce global system properties from local ones, or vice-versa. That way data, observations, and hypotheses at different scales (e.g., observations of forests vs. observations of tissues in a lab) can be related in a systematic way.
Anyways, that's how I ended up here.