Department of Mathematics: Graduate Seminar Series

Fully extended reflection-positive invertible field theories serve as homotopical models for symmetry-protected topological phases in physics. To study fermionic SPTs, we use invertible field theories on manifolds with twisted spin structures encoded by fermionic groups, allowing us to compare with K-theoretic classifications of free fermion SPTs. We carry out computations in the interesting example case of the "Bott spiral" studied by Queiroz--Khalaf--Stern, which highlights several subtleties, including that the twisted spin structure produced from a fermionic group is not an invariant of the Morita class of the fermionic group superalgebra.