This 4-day school is aimed at PhD students, postdocs and advanced master’s students in mathematics. It will give an introduction to the theory of characteristic classes, starting with vector bundles and leading to more advanced topics such as the Hirzebruch signature theorem and Milnor’s exotic seven-dimensional spheres.
The programme roughly follows Milnor and Stasheff’s Characteristic Classes and Hatcher’s Vector Bundles and K-Theory.
Format
The school consists of eleven talks, prepared and given by participants. Each speaker receives a detailed outline specifying the material to cover, including which results to prove and which to treat as a black box. Organizers are available before and during the event to help speakers prepare. We hope to make the school a friendly place to learn together, where questions, including basic ones, will be very welcome.
Programme
- Vector bundles and Stiefel–Whitney classes
- Classifying spaces of vector bundles
- The Leray–Hirsch theorem, construction of Stiefel–Whitney and Chern classes, and the splitting principle
- The Thom isomorphism, Euler classes and the Gysin sequence
- The cohomology of Grassmannians
- Pontryagin classes and characteristic numbers
- Cobordism and the Pontryagin–Thom theorem
- The Hirzebruch signature theorem
- Milnor’s exotic 7-sphere
- Topological K-theory and the Chern character
- Chern–Weil theory
More details can be found here:
Winter school talk descriptions
Lightning talks
We also plan to have informal 5-minute lightning talks where participants can briefly share their current research interests.
Registration
Participants is free, but registration is required. Deadline: 1 November 2026.
Organisers
Achim Krause, John Christian Ottem, Jørgen Rennemo and Kris Shaw.
The event is sponsored by the RCN Grant NORSTAGE.