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SUMMARY:Bernhard Keller (Université de Paris)
DTSTART:20200925T130000Z
DTEND:20200925T134000Z
DTSTAMP:20260423T004639Z
UID:SheRepTh/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SheRepTh/1/"
 >Cartan matrices and Calabi-Yau completions</a>\nby Bernhard Keller (Unive
 rsité de Paris) as part of Sherbrooke Meeting on Representation Theory of
  Algebras\, Corona Edition (fully online)\n\n\nAbstract\nQuantum Cartan ma
 trices and their inverses are of interest in the representation theory of 
 quantum affine algebras. We show how to\ncategorify them for simply laced 
 Dynkin diagrams using bigraded\nCalabi-Yau completions (aka bigraded Ginzb
 urg algebras). In particular\, we will recover a formula due to Hernandez-
 Leclerc (2015) and\nFujita (2019) expressing the inverse quantum Cartan ma
 trix in\nterms of the (ordinary) derived category and thus in terms of the
  combinatorics of the repetition quiver. We will end by discussing\nthe pr
 oblem of obtaining analogous results in the non simply laced case.\n
LOCATION:https://researchseminars.org/talk/SheRepTh/1/
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