About
This is an undergraduate student seminar on geometry and topology. Here is a course description for you to get an idea of how it runs and particularly for those of you who wish to register for credit. If you would like to propose a topic in geometry and topology for now or the future, write to Yifei Zhu.
Our theme for Spring 2026 is Riemann surfaces. We meet on Fridays 4:20–6:10 in Chi Wah 304.
Schedule
Mar 6, '26,
Hongli Ye,
Riemann surfaces and their basic properties
Mar 13, '26,
Xuan Wu,
Covering maps
Mar 20, '26, Zhenyuan Dai, Analytic continuation and algebraic functions
Mar 27, '26, Zhenyuan Dai, Analytic continuation and algebraic functions, cont'd
Apr 3, '26, Hongli Ye, Differential forms and integration
Apr 10, '26, Xuan Wu
Apr 17, '26, Xuan Wu
Apr 24, '26, Boran Ding
May 8, '26, Yang Rong, Riemann–Roch
May 15, '26, Yang Rong, Serre duality
May 22, '26, Wendi Zheng
May 29, '26, Dan Zhu
Jun 5, '26, TBD
References
- Otto Forster, Lectures on Riemann surfaces
- Rick Miranda, Algebraic curves and Riemann surfaces
- J.S. Milne, Modular functions and modular forms (elliptic modular curves), Section I.2
- Danny Calegari, What is Teichmüller theory?
- Alex Wright, Moduli spaces of Riemann surfaces
Previous Semesters
- Fall 2025, Geometric models and their additive engineering
- Fall 2024, Geometry and physics of Higgs bundles
- Fall 2023, Modular curves
- Spring 2023, Knot theory and low-dimensional topology
- Fall 2022, Modular forms and their applications to geometry and topology
- Spring 2022, Topological data analysis
- Fall 2021, Differential forms in algebraic topology
- Spring 2021, The wild world of 4-manifolds
- Even earlier, we worked on Manifolds, sheaves, and cohomology and more.