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SUMMARY:On the Grassmannian root conjecture
DTSTART:20260902T150000Z
DTEND:20260902T160000Z
DTSTAMP:20260910T060800Z
UID:indico-event-17092@indico.math.cnrs.fr
CONTACT:kellendonk@math.univ-lyon1.fr\;athomas@math.univ-lyon1.fr
DESCRIPTION:Speakers: Bernhard Keller (IMJ-PRG)\n\nIn 2016\, Jensen–King
 –Su introduced an (infinite-dimensional\, noncommutative) Gorenstein alg
 ebra whose category of Cohen–Macaulay modules categorifies the cluster s
 tructure on the Grassmannian of k-dimensional subspaces in n-dimensional s
 pace. Among other results\, they obtained a map taking each cluster monomi
 al to an element of the root lattice of the tree  with three branches of 
 lengths k\, n-k and 2. They conjectured that the images of the cluster var
 iables are roots and checked this for the cases where J_{k\,n} is a Dynkin
  diagram. Baur–Bogdanić–García Elsener and Baur–Bogdanić–Garcí
 a Elsener–Li (preprint) confirmed the conjecture in many other cases in 
 2020. In this largely expository talk\, we will provide further evidence f
 or the conjecture. This is a report on ongoing joint work with Sarjick Bak
 shi\, Mingfa Chen and Haoyu Wang.\n\nhttps://indico.math.cnrs.fr/event/170
 92/
LOCATION:Salle Fokko du Cloux (Bat. Braconnier)
URL:https://indico.math.cnrs.fr/event/17092/
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