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.

Our theme for Fall 2025 is geometric models and their additive engineering, such as this and this. We have 3D printers handy in Research Building 3 thanks to support by the Department of Mathematics and the National Center for Applied Mathematics Shenzhen. Here are some additional suggestions and references in case you don't have a favorite example in mind yet!

We meet on Thursday/Friday in alternating weeks 4:30–5:30 pm (see schedule below) in College of Science M5024.

Schedule

Sep 11, '25, 4:20 pm in College of Science M5024, Organizational meeting

Fri Sep 19, '25, Yifei Zhu, Swallowtails (context and theory)

Thu Sep 25, '25 (Research Building 3, 9th floor, access the building from Entrance D2 at ground level), Yifei Zhu, Swallowtails (engineering)

Thu Oct 9, '25, Xuan Wu and Pujin Ye, Knots (context and theory)

Wed Oct 15, '25, Training session

Fri Oct 17, '25, Xuan Wu and Pujin Ye, Knots (engineering)

Thu Oct 23, '25, Liuyuan Chen and Tianlin Gao, Riemann surfaces (context and theory)

Fri Nov 14, '25, Liuyuan Chen and Tianlin Gao, Riemann surfaces (engineering)

Thu Nov 20, '25, Youkang Gong and Qirui Huang, Stereographic projection and tessellations (context and theory)

Fri Nov 28, '25, Youkang Gong and Qirui Huang, Stereographic projection and tessellations (engineering)

Thu Dec 4, '25, Yanche Wu and Xiuyuan Yang, Poincaré homology sphere (context and theory)

Fri Dec 12, '25, Yanche Wu and Xiuyuan Yang, Poincaré homology sphere (engineering)

Thu Dec 18, '25, Hongli Ye, Minimal surfaces (context and theory)

Fri Dec 26, '25, Hongli Ye, Minimal surfaces (engineering)

Previous Semesters

  • 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.