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孙 哲 博士:McShane identities for Higher Teichmuller theory and the Goncharov-Shen potential

本站小编 Free考研考试/2021-12-26


Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
Speaker: 孙 哲 博士，IHES
Inviter:
Title:
 McShane identities for Higher Teichmuller theory and the Goncharov-Shen potential
Time & Venue:
 2021.05.13 20:00-22:00 腾讯会议:667340431 (密码：2021)
Abstract:
 McShane established a remarkable identity for the lengths of simple closed geodesics on the hyperbolic surface with cusps. Mirzakhani extended McShane identity to obtain a beautiful recursive formula for the volumes of the moduli spaces of Riemann surface, which again proved the Witten-Kontsevich theorem. Joint with Yi Huang, we found a collection of new McShane-type identities parameterized by the pairs (cusp/hole, simple positive root), which are the right analogs of McShane/Mirzakhani identities in the case of higher rank Lie groups, and provided us some expectations to generalize Mirzakhani's recursive formula to the higher rank case. I will also explain some interesting applications.

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