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

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

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

Yoichi Imayoshi, Masahiko Taniguchi, An Introduction to Teichmüller Spaces

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

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

Andrew J. Casson and Steven A. Bleiler, Automorphisms of surfaces after Nielsen and
Thurston, London Mathematical Society Student Texts, vol. 9, Cambridge University

Press, Cambridge, 1988.

R. C. Penner and J. L. Harer, Combinatorics of train tracks, Annals of Mathematics
Studies, vol. 125, Princeton University Press, Princeton, NJ, 1992.

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。