There are three sources of commutative algebras: algebras of functions on
spaces, cohomology algebras (when the odd degree cohomology is absent), algebras of
Hamiltonians of quantum integrable models. I will discuss an example of an algebra
which appears in each of these three aspects.
Links:
[1] https://www.mpim-bonn.mpg.de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/node/5312