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SUMMARY:Simple-mindedness in negative Calabi-Yau cluster categories of the
  hereditary type - Raquel Coelho Simoes (Lancaster University - Mathematic
 s and Statistic Dept.)
DTSTART:20211123T160000Z
DTEND:20211123T170000Z
UID:TALK164866@talks.cam.ac.uk
DESCRIPTION:Simple-minded systems were introduced by Koenig-Liu as an abst
 raction of non-projective simple modules in stable module categories. In t
 his talk\, we will consider simple-minded systems in certain orbit categor
 ies of the bounded derived category of a hereditary algebra\, which can be
  considered to be negative Calabi-Yau cluster categories. Simple-minded sy
 stems in this setting turn out to play the role of cluster-tilting objects
  in the positive Calabi-Yau setup. We will give a bijection between simple
 -minded systems\, simple-minded collections in the fundamental domain and 
 positive (higher) noncrossing partitions. These results generalise the res
 ults of Iyama-Jin for Dynkin type. This is based on joint work with David 
 Pauksztello and David Ploog.
LOCATION:Seminar Room 2\, Newton Institute
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