Friday, December 4, 2020
12/04/2020 - 1:00pm
We construct and study cluster algebra structures in rings of invariants of the special linear group action on collections of three-dimensional vectors, covectors, and matrices. The construction uses Kuperberg’s calculus of webs on marked surfaces with boundary. We then proceed to interpret webs as straightedge constructions in plane projective geometry. In both cluster side and projective geometry side of the story an important role is played by the arborization algorithm that we introduce. This is joint work with Sergey Fomin.