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SUMMARY:Eleonore Faber (University of Leeds)
DTSTART:20220429T120000Z
DTEND:20220429T130000Z
DTSTAMP:20260423T020953Z
UID:VCAS/132
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/VCAS/132/">C
 luster structures for the A-infinity singularity</a>\nby Eleonore Faber (U
 niversity of Leeds) as part of IIT Bombay Virtual Commutative Algebra Semi
 nar\n\n\nAbstract\nThis talk is about a categorification of the coordinate
  rings of Grassmannians\nof infinite rank in terms of graded maximal Cohen
 -Macaulay modules over the ring $\\mathbb{C}[x\,y]/(x^k).$ This yields an 
 infinite rank analog of the Grassmannian cluster categories introduced by 
 Jensen\, King\, and Su.\nIn the special case\, $k=2\,$ $\\text{Spec}(\\mat
 hbb{C}[x\,y]/(x^2))$ is a type $A$-infinity singularity and the ungraded v
 ersion of the category of maximal Cohen-Macaulay modules over $\\mathbb{C}
 [x\,y]/(x^2))$ has been studied by Buchweitz\, Greuel\, and Schreyer in th
 e 1980s. We demonstrate that his category has infinite type $A$ cluster co
 mbinatorics. In particular\, we show that it has cluster-tilting subcatego
 ries modeled by certain triangulations of the (completed) infinity-gon and
  we can also interpret certain mutations of the category in this model. Th
 is is joint work with Jenny August\, Man-Wai Cheung\, Sira Gratz\, and Sib
 ylle Schroll.\n
LOCATION:https://researchseminars.org/talk/VCAS/132/
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