课程介绍：1. Representation of fundamental groups of surfaces, fiber bundles, connections 2. Cohomology and torsion 3. Character variety 4. Symplectic structure 5. Volumes of moduli spaces of Riemann surfaces, multicurves counting and intersection theory 6. Cluster algebra and positive representations 7. Primarily on the geometry and topology of three-manifolds 8. Skein algebras, quantum groups and 3D quantum invariants 9. Chern-Simons 10. Higgs bundles, harmonic maps 11. Anosov representations

上课地点：2409

上课时间：周二四15：55-17：30

考试形式：Report

面向对象：master/phd students

授课教师：孙哲

开课学年：2023-2024

开课学期：秋学期

课程号：MATH7429P.01

学分：4.0

课程类型：研究生课程

是否精品课程：否

课时：80.0

教材及参考书：François Labourie, Lectures on Representations of Surface Groups Maryam Mirzakhani, Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces Vladimir Fock, Alexander Goncharov, Moduli spaces of local systems and higher Teichmüller theory William P. Thurston, The Geometry and Topology of Three-Manifolds Richard D. Canary, Anosov representations: informal lecture notes Richard Wentworth, Higgs Bundles and Local Systems on Riemann Surfaces