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SUMMARY:Thomas Lam (University of Michigan)
DTSTART:20210113T000000Z
DTEND:20210113T005000Z
DTSTAMP:20260423T005655Z
UID:LCM2021/31
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LCM2021/31/"
 >Positroid varieties and  $q\,t$ -Catalan numbers</a>\nby Thomas Lam (Univ
 ersity of Michigan) as part of Legendrians\, Cluster algebras\, and Mirror
  symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n\nAbst
 ract\nPositroid varieties are subvarieties of the Grassmannian defined as 
 intersections of rotations of Schubert varieties in my work with Knutson a
 nd Speyer. They also appear in the work of Shende-Treumann-Williams-Zaslow
  as moduli spaces of constructible sheaves with microsupport in a Legendri
 an link. $\\newline$\nWe show that the "top open positroid variety" has mi
 xed Hodge polynomial given by the  $q\,t$-rational Catalan numbers (up to 
 a simple factor). The $q\,t$-rational Catalan numbers satisfy remarkable s
 ymmetry and unimodality properties\, and we show that these follow from th
 e curious Lefschetz phenomenon for cluster varieties. The cohomologies of 
 open positroid varieties are shown to be related to Khovanov-Rosanzky knot
  homology.$\\newline$\nThis talk is based on joint work with Pavel Galashi
 n.\n
LOCATION:https://researchseminars.org/talk/LCM2021/31/
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