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.
The theme for Fall 2026 is group cohomology in geometry, topology, algebra, and number theory. We meet on Fridays 10:20–12:10 in Chi Wah 116.
Schedule
Sep 18, '26, Organizational meeting
Oct 9, '26, Qinpei Huang, Defining group homology and cohomology
Oct 16, '26, Qinpei Huang, Defining group homology and cohomology, II
Oct 23, '26, Qinpei Huang, Defining group homology and cohomology, III
Oct 30, '26, Boran Ding, Examples: cyclic groups
Nov 6, '26, Wendi Zheng, $K(G,1)$ and classifying spaces
Nov 13, '26, Xuan Wu, Galois cohomology
References
- Charles A. Weibel, An Introduction to Homological Algebra, Chapter 6
- Braid groups, configurations spaces, homological stability: Rita Jiménez Rolland, Jennifer C. H. Wilson, Stability properties of moduli spaces (2022) V.I. Arnold, Braids of algebraic functions and the cohomology of swallowtails (1968) translated by Gerald Gould
- Galois groups, continuous cohomology of profinite groups, condensed mathematics: Romyar Sharifi, Group and Galois cohomology Peter Scholze, Lectures on condensed mathematics (2019, updated 2026)
- (Special) orthogonal groups, (special) unitary groups, (s)pin groups, classifying spaces, characteristic classes, spectral sequences: Allen Hatcher, Algebraic Topology, Sections 3.D and 4.D John McCleary, A User's Guide to Spectral Sequences, Section 6.3
- General linear groups: Peter Patzt, Thomas Willwacher, The graph complex and the homology of the general linear groups revisited
Previous Semesters
- Spring 2026, Riemann surfaces
- 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.