Department of Mathematics

Geometry and Topology

  •  Peng Zhou, Berkeley
  •  Homological Mirror Symmetry for A_n-type cluster varieties
  •  09/28/2021
  •  4:00 PM - 5:00 PM
  •  Online (virtual meeting) (Virtual Meeting Link)
  •  Honghao Gao (

The A_n type cluster variety, denoted by X_n, is the affine scheme associated to the upper cluster algebra of the A_n quiver (of n unfrozen vertices and one frozen vertex). The dual of X_n is denoted as Y_n, and is isomorphic but not canonically to X_n. For example, the variety X_1 is given by the equation {x y = 1 + q} where x, y are in \C and q is in \C^*. We prove that the homological mirror symmetry (HMS) conjecture for X_n, Y_n: the coherent sheaf category of Coh(X_n) is equivalent to the wrapped Fukaya category WFuk(Y_n), generalizing the known case for n=1 and 2. This is based on a recent work of Gammage-Le on HMS for truncated cluster variety, by putting back the 'truncated' part. This is work in progress, and is joint with Linhui Shen and Zhe Sun.



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science