Department of Mathematics

Geometry and Topology

  •  Chris Fraser, MSU
  •  Braid group action on Grassmannian cluster varieties and spherical twists
  •  09/21/2021
  •  4:00 PM - 5:00 PM
  •  Online (virtual meeting) (Virtual Meeting Link)
  •  Honghao Gao (gaohongh@msu.edu)

I will exhibit an action of the d-strand extended affine braid group on the top-dimensional positroid variety in the Grassmannian Gr(k,n), where d = gcd(k,n). Roger Casals and Honghao Gao showed that this action can be used to exhibit infinitely many distinct Lagrangian fillings of (most) Legendrian torus knots. The braid group action is compatible with the cluster variety structure on Gr(k,n). Finally, I will discuss joint work in progress with Bernhard Keller which interprets this action as a composition of spherical twists in bounded derived categories which additively categorify the cluster algebra.

 

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