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SUMMARY:Daping Weng (Michigan State University)
DTSTART:20210108T010000Z
DTEND:20210108T020000Z
DTSTAMP:20260423T024448Z
UID:LCM2021/21
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LCM2021/21/"
 >Examples of cluster varieties from plabic graphs III</a>\nby Daping Weng 
 (Michigan State University) as part of Legendrians\, Cluster algebras\, an
 d Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.
 \n\nAbstract\nCluster varieties were introduced by Fock and Goncharov as g
 eometric counterparts of Fomin and Zelevinsky’s cluster algebras. Simply
  speaking\, cluster varieties are algebraic varieties with an atlas of tor
 us charts\, whose transition maps are captured by certain combinatorial pr
 ocess called cluster mutations. Many interesting geometric objects turn ou
 t to be examples of cluster varieties\, and one can then use cluster theor
 etical techniques to study these geometric objects. In this lecture series
 \, we will discuss various examples of cluster varieties whose combinatori
 cs can be captured by plabic graphs\, including Grassmannians and double B
 ruhat/Bott-Samelson cells of $SL_n$. This lecture series will be complemen
 tary to Linhui Shen’s lecture series on cluster theory.\n\nLecture 3: do
 uble Bruhat cells of $SL_n$ $\\newline$\nWe introduce double Bruhat cells 
 of a semisimple Lie group and discuss the cluster structures on double Bru
 hat cells of $SL_n$ in terms of plabic graphs.\n
LOCATION:https://researchseminars.org/talk/LCM2021/21/
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