我非常赞同梁永祺老师关于研究生的指导：https://faculty.ustc.edu.cn/yqliang/files/teaching.htm#general

本方向研究生初步科目与参考书目（参考但不限于）

黎曼曲面

Peter Buser, Geometry and Spectra of Compact Riemann Surfaces

https://link.springer.com/book/10.1007/978-0-8176-4992-0

Otto Forster, Lectures on Riemann Surfaces

https://link.springer.com/book/10.1007/978-1-4612-5961-9

Teichmuller理论

Yoichi Imayoshi, Masahiko Taniguchi, An Introduction to Teichmüller Spaces

https://link.springer.com/book/10.1007/978-4-431-68174-8

Benson Farb and Dan Margalit, A Primer on Mapping Class Groups

http://euclid.nmu.edu/~joshthom/Teaching/MA589/farbmarg.pdf

李群李代数及其表示

Alexander Kirillov, Introduction to Lie Groups and Lie Algebras

https://www.math.stonybrook.edu/~kirillov/liegroups/

Anthony W. Knapp, Lie Groups Beyond an Introduction

https://www.math.stonybrook.edu/~aknapp/download.html

丛代数

Introduction to Cluster Algebras

https://arxiv.org/abs/1608.05735

https://arxiv.org/abs/1707.07190

https://arxiv.org/abs/2008.09189

https://arxiv.org/abs/2106.02160

低维几何拓扑

William P. Thurston, The Geometry and Topology of Three-Manifolds

https://www.math.unl.edu/~jkettinger2/thurston.pdf

Robion C. Kirby, The Topology of 4-Manifolds

https://link.springer.com/book/10.1007/BFb0089031

曲面分层与二次微分

Albert Fathi, François Laudenbach and Valentin Poénaru, Thurston's Work on Surfaces

https://www.degruyter.com/document/doi/10.1515/9781400839032/html#overview

 Viveka Erlandsson, Juan Souto, Mirzakhani’s Curve Counting and Geodesic Currents

https://link.springer.com/book/10.1007/978-3-031-08705-9

Kurt Strebel, Quadratic Differentials

https://link.springer.com/chapter/10.1007/978-3-662-02414-0_2

代数拓扑

Allen Hatcher, Algebraic Topology

https://pi.math.cornell.edu/~hatcher/AT/ATpage.html

微分几何

J. Milnor, Morse theory

https://www.uio.no/studier/emner/matnat/math/MAT9580/v17/documents/morse-theory.pdf

MICHAEL SPIVAK, A Comprehensive Introduction to Differential Geometry 1,2,3,4,5

https://luis.impa.br/aulas/anvar/Spivak_Vol1_3ed.pdf

模空间

Joe Harris , Ian Morrison, moduli of curves

https://link.springer.com/book/10.1007/b98867

William Fulton, Algebraic Curves: An Introduction to Algebraic Geometry

https://dept.math.lsa.umich.edu/~wfulton/CurveBook.pdf

Enrico Arbarello , Maurizio Cornalba , Phillip A. Griffiths, Geometry of Algebraic Curves

https://link.springer.com/book/10.1007/978-1-4757-5323-3

https://link.springer.com/book/10.1007/978-3-540-69392-5

进一步参考书目在

https://faculty.ustc.edu.cn/sunzhe1/zh_CN/skxx/661152/content/3163.htm#skxx

找我读博士需要在黎曼曲面，Teichmuller理论，李群李代数及其表示，丛代数，曲面分层，低维几何拓扑，代数拓扑、微分几何，模空间这些科目中，学过至少3门，较为深刻的理解并掌握至少2门或者很深刻的理解其中1门。