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SUMMARY:Daping Weng (Michigan State University)
DTSTART:20210107T010000Z
DTEND:20210107T020000Z
DTSTAMP:20260423T005656Z
UID:LCM2021/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LCM2021/17/"
 >Examples of cluster varieties from plabic graphs I</a>\nby Daping Weng (M
 ichigan 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 geo
 metric counterparts of Fomin and Zelevinsky’s cluster algebras. Simply s
 peaking\, cluster varieties are algebraic varieties with an atlas of torus
  charts\, whose transition maps are captured by certain combinatorial proc
 ess called cluster mutations. Many interesting geometric objects turn out 
 to be examples of cluster varieties\, and one can then use cluster theoret
 ical techniques to study these geometric objects. In this lecture series\,
  we will discuss various examples of cluster varieties whose combinatorics
  can be captured by plabic graphs\, including Grassmannians and double Bru
 hat/Bott-Samelson cells of $SL_n$. This lecture series will be complementa
 ry to Linhui Shen’s lecture series on cluster theory.\n\nLecture 1: $Gr(
 2\,n)$ and $M(0\,n)$ $\\newline$\nWe discuss the cluster structures on Gra
 ssmannian $Gr(2\,n)$ and on the moduli space of $n$ points in $\\mathbb{P}
 ^1$. These are examples of cluster varieties of Dynkin $A_{n-3}$ mutation 
 type and their combinatorics are captured by triangulations of an $n$-gon.
 \n
LOCATION:https://researchseminars.org/talk/LCM2021/17/
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