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SUMMARY:Linhui Shen (Michigan State University)
DTSTART:20210112T010000Z
DTEND:20210112T015000Z
DTSTAMP:20260423T005722Z
UID:LCM2021/29
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LCM2021/29/"
 >Quantum geometry of moduli spaces of local systems</a>\nby Linhui Shen (M
 ichigan State University) as part of Legendrians\, Cluster algebras\, and 
 Mirror symmetry\n\nLecture held in POSTECH\, Pohang\, Republic of Korea.\n
 \nAbstract\nLet $G$ be a split semi-simple algebraic group over $\\mathbb{
 Q}$. We introduce a natural cluster structure on moduli spaces of $G$-loca
 l systems over surfaces with marked points. As a consequence\, the moduli 
 spaces of $G$-local systems admit natural Poisson structures\, and can be 
 further quantized. We will study the principal series representations of s
 uch quantum spaces. It will recover many classical topics\, such as the $q
 $-deformed Toda systems\, quantum groups\, and the modular functor conject
 ure for such representations. This talk will mainly be based on joint work
  with A.B. Goncharov.\n
LOCATION:https://researchseminars.org/talk/LCM2021/29/
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