Behind the Scenes

The Dean of the College of Arts and Sciences is a mathematician. With his administrative duties, he doesn't get as much time as he'd like to work on and talk about mathematics, but he does grab opportunities when he can. Yesterday he gave a departmental colloquium talk, on the algebraic analysis of Markov chains. That's off in the borderland between combinatorics and probability theory, far distant from my work on the classification of polygons.

Listening to him, though, was surprising. We're using the same, or very similar, tools in our different areas. We're both using group algebras (he's going me one better, looking also at semigroup algebras), and the stochastic matrices he's working with, viewed from the right angle, bear a strong resemblance to my central weighted transforms (although mine are a bit more broadly defined).

I mentioned this to him after the talk, and he wants to see some of it written up - but most of that comes from my work on G-gons, which I haven't written up, and can't, for the time being. But maybe we'll sit down sometime and chat about it.

This is, in large measure, what mathematics is about: identifying commonalities and studying their implications, showing connections between disparate fields. I'm wondering if what he's doing might have some application to my work. I don't see how as yet, but you never know...