中科院数学与系统科学研究院

数学研究所

中科院华罗庚数学重点实验室

华罗庚青年数学论坛

学术报告

报告人：孙 哲 博士（IHES）

题  目： Introduction to higher teichmuller theory

时  间：2021.05.11（星期二），20:00-21:00

地  点：腾讯会议810450272 (密码：2021)

摘  要：Higher Teichmuller theory is the study of special components of representations spaces of fundamental groups of surface into higher rank Lie groups. In this talk, I will introduce the higher Teichmuller theory and relevant conjectures from some different aspects.

-----------------------------------------------------------------------------------------------------------------------
  报告人：孙 哲 博士（IHES）

题  目：McShane identities for Higher Teichmuller theory and the Goncharov-Shen potential

时  间：2021.05.13（星期四），20:00-22:00

地  点：腾讯会议667340431 (密码：2021)

摘  要：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.

-------------------------------------------------------------------------------------------------------------------------
  报告人：孙 哲 博士 （IHES）

题  目：3-webs and Fock--Goncharov duality conjecture

时  间：2021.05.18（星期二），20:00-22:00

地  点：腾讯会议465970954 (密码：2021)

摘  要：Fock--Goncharov duality conjecture says that the canonical linear basis of the regular function ring of one space can be parameterized by the tropical integer points of the dual space.  Joint with Daniel Douglas, we parameterized the trace function linear basis of the SL_3 character variety by some tropical integer points of Fock--Goncharov A moduli space satisfying the Kuntson-Tao inequalities. The crucial tools are the Kuperberg 3-webs which are oriented 3-valent graphs on the surface which I will explain in more detail.