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SUMMARY:Boundary algebras arising from uniform Postnikov diagams on surfac
 es - Colin Krawchuk
DTSTART:20211201T163000Z
DTEND:20211201T173000Z
UID:TALK165052@talks.cam.ac.uk
CONTACT:Stacey Law
DESCRIPTION:A Postnikov diagram is an embedding of oriented curves\, calle
 d strands\, in a disk. These diagrams are known to describe the cluster al
 gebra structure of open positroid varieties\, with diagrams of uniform typ
 e corresponding to a cluster of minors in the Grassmannian Gr(k\,n). Each 
 Postnikov diagram can be associated with a dimer algebra\, which is the Ja
 cobian algebra of a quiver with potential. Baur-King-Marsh showed that the
  opposite of the boundary algebra corresponding to such a dimer algebra is
  isomorphic to a quotient of the preprojective algebra used by Jensen-King
 -Su to categorify the cluster structure of Gr(k\,n). They also determined 
 the boundary algebra for degree two weak Postnikov diagrams arising from g
 eneral surfaces. This talk will discuss a combinatorial approach to calcul
 ating the boundary algebra associated to a uniform Postnikov diagram\, and
  how this can be translated to Postnikov diagrams on other surfaces. \n\n
LOCATION:MR12
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