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SUMMARY:Daping Weng (Michigan State University)
DTSTART:20210107T020000Z
DTEND:20210107T030000Z
DTSTAMP:20260423T005717Z
UID:LCM2021/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LCM2021/20/"
 >Examples of cluster varieties from plabic graphs II</a>\nby Daping Weng (
 Michigan State University) as part of Legendrians\, Cluster algebras\, and
  Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\
 n\nAbstract\nCluster varieties were introduced by Fock and Goncharov as ge
 ometric counterparts of Fomin and Zelevinsky’s cluster algebras. Simply 
 speaking\, cluster varieties are algebraic varieties with an atlas of toru
 s charts\, whose transition maps are captured by certain combinatorial pro
 cess called cluster mutations. Many interesting geometric objects turn out
  to be examples of cluster varieties\, and one can then use cluster theore
 tical techniques to study these geometric objects. In this lecture series\
 , we will discuss various examples of cluster varieties whose combinatoric
 s can be captured by plabic graphs\, including Grassmannians and double Br
 uhat/Bott-Samelson cells of $SL_n$. This lecture series will be complement
 ary to Linhui Shen’s lecture series on cluster theory.\n\nLecture 2: pla
 bic graphs and $Gr(k\,n)$ $\\newline$\nWe introduce plabic (planar bicolor
 ) graphs and use them to describe the cluster structures on Grassmannian $
 Gr(k\,n)$ and on the moduli space of $n$ points on $\\mathbb{P}^{k-1}$.\n
LOCATION:https://researchseminars.org/talk/LCM2021/20/
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