BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Hironori Oya (Tokyo Institute of Technology)
DTSTART:20221222T010000Z
DTEND:20221222T023000Z
DTSTAMP:20260423T022055Z
UID:gapkias/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/gapkias/3/">
 Wilson lines on the moduli space of $G$-local systems on a marked surface<
 /a>\nby Hironori Oya (Tokyo Institute of Technology) as part of Geometry\,
  Algebra and Physics at KIAS\n\n\nAbstract\nFor a marked surface $\\Sigma$
 \, there are two kinds of extensions of moduli spaces of local systems on 
 $\\Sigma$\, written as $\\mathcal{A}_{\\widetilde{G}\, \\Sigma}$ and $\\ma
 thcal{P}_{G\, \\Sigma}$\, where $\\widetilde{G}$ is a connected simply-con
 nected complex simple algebraic group and $G=\\widetilde{G}/Z(\\widetilde{
 G})$ its adjoint group. These are introduced by Fock--Goncharov and Goncha
 rov--Shen respectively\, and it is known that the pair $(\\mathcal{A}_{\\w
 idetilde{G}\, \\Sigma}\, \\mathcal{P}_{G\, \\Sigma})$ forms a cluster ense
 mble.\n  In this talk\, we formulate a class of $\\widetilde{G}$ or $G$-va
 lued morphisms defined on these moduli spaces\, which we call Wilson lines
 . I explain their basic properties and application. In particular\, we giv
 e an affirmative answer to the $\\mathrm{A}=\\mathrm{U}$ problem for the c
 luster algebras arising from the cluster $K_2$-structures on $\\mathcal{A}
 _{\\widetilde{G}\, \\Sigma}$ under some assumptions on $G$ and $\\Sigma$.\
 n  This talk is based on a joint work with Tsukasa Ishibashi and Linhui Sh
 en.\n
LOCATION:https://researchseminars.org/talk/gapkias/3/
END:VEVENT
END:VCALENDAR