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SUMMARY:Generalized Mcshane's Identity via Landau-Ginzberg Potential and T
riple Ratios
DTSTART;VALUE=DATE-TIME:20180313T133000Z
DTEND;VALUE=DATE-TIME:20180313T143000Z
DTSTAMP;VALUE=DATE-TIME:20190618T152126Z
UID:indico-event-3328@indico.math.cnrs.fr
DESCRIPTION:(Joint work with Yi Huang) Goncharov and Shen introduced a Lan
dau-Ginzberg potential on the Fock-Goncharov $A_{G\,S}$ moduli space\, whe
re $G$ is a semisimple Lie group and $S$ is a ciliated surface. They used
the potential to formulate a mirror symmetry via Geometric Satake Correspo
ndence. This potential is the markoff equation for $A_{ PSL(2\,R)\, S_{1\,
1} }$. When $S=S_{g\,m}$\, such potential can be written as a sum of rank
$G*m$ partial potentials. We obtain a family of generalized Mcshane's iden
tities by splitting these partial potentials for $A_{PSL(n\,R)\,S_{g\,m}}$
by certain pattern of cluster transformations with geometric meaning. We
also find some interesting new phenomena in higher rank case\, like triple
ratio is bounded in mapping class group orbit. As applications\, we find
a generalized collar lemma which involves $\\lambda 1 / \\lambda 2$ length
spectral\, discreteness of that spectral etc. In further research\, we wo
uld like to ask how can we integrate to obtain the generalized Mirzakhani'
s topological recursion with $\\mathcal{W}_n$ constraint?\n\nhttps://indic
o.math.cnrs.fr/event/3328/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/3328/
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