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SUMMARY:Daping Weng (UC Davis)
DTSTART:20211102T180000Z
DTEND:20211102T190000Z
DTSTAMP:20260423T024649Z
UID:AG-Davis/38
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AG-Davis/38/
 ">Cyclic Sieving and Cluster Duality for Grassmannian</a>\nby Daping Weng 
 (UC Davis) as part of UC Davis algebraic geometry seminar\n\n\nAbstract\nF
 or any two positive integers a and b\, the homogeneous coordinate ring of 
 Gr(a\,a+b) is isomorphic to a direct sum over all irreducible GL(a+b) repr
 esentations associated with weights that are multiples of w_a. Following a
  result of Scott\, the homogeneous coordinate ring of a Grassmannian has t
 he structure of a cluster algebra. The Fock-Goncharov cluster duality conj
 ecture states that an (upper) cluster algebra admits a cluster canonical b
 asis parametrized by the tropical integer points of the dual cluster varie
 ty. In a joint work with L. Shen\, we introduce a periodic configuration s
 pace of lines as the cluster dual for Gr(a\,a+b). We equip this cluster du
 al with a natural potential function W and obtain a cluster canonical basi
 s for Gr(a\,a+b)\, parametrized by plane partitions. As an application\, w
 e prove a cyclic sieving phenomenon of plane partitions under a certain to
 ggling sequence.\n
LOCATION:https://researchseminars.org/talk/AG-Davis/38/
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