New year

Happy new year! In my case, this is the first that I’ve spent outside the UK. I have been at 10700 feet on a mountain in Colorado for the last two weeks and have some poetry to prove it. The four poems Halves, Vast, Commonality, and Cycle form my `Colorado period’. I’ve also charted out the Dynkin correspondences that I am aware of for my own convenience. For those who haven’t suffered a monologue from me about them, Dynkin diagrams are a class of finite graphs/quivers that solve a remarkable number of classification problems. This common parameterisation allows one to link the various objects parameterised in an `abstract’ way, however there is often something geometrical underlying these coincidences. The most recent Dynkin classification I know about is that of finite-type cluster algebras by Fomin and Zelevinsky. A natural thing to attempt, then, is to incorporate this cluster classification into the web of Dynkin correspondences. This is a note outlining the existing correspondences that I know of. You will observe that it is very incomplete. I am currently thinking about how to convincingly (= geometrically) extend the fingers of cluster algebras into many of the other pies admitting Dynkin classifications.


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