Topic: homotopy theory

Summing over spin structures in quantum field theory can be obstructed by a mod-16 anomaly extending the familiar fermion-parity anomaly. This talk uses homotopy theory and cobordism-group cohomology to explain the obstruction, its consequences for operations such as the GSO projection and dualities, and extensions involving other dimensions, symmetries and symmetry topological field theories.

Zhouli Xu explains the Kervaire invariant problem and the role of unusual geometric objects in high-dimensional topology. He describes the long route towards resolving the problem in dimension 126, including the collaborative and technical challenges behind the proof. The conversation was recorded during the Isaac Newton Institute programme on equivariant homotopy theory.