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GDMSeminar: Abstracts of the Talks (2022/3)

Anton Izosimov  (University of Arizona)
Polygon recutting

Tuesday, March 1, 2022, 16:00 GMT

Abstract: Recutting is an operation on planar polygons defined by cutting a polygon along a diagonal to remove a triangle, and then reattaching the triangle along the same diagonal but with opposite orientation (V. Adler, 1993). Recuttings along different diagonals generate an action of the affine symmetric group on the space of polygons. I will explain my recent proof of complete integrability of that action, and in particular discuss its relation to quaternionic polynomials and cluster algebras.