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Monday, September 28, 2015

**Abstract:** This talk is about a pair of coincidences in homotopy theory which related quantum field theory with commutative algebra. The first coincidence is the fact that the etale homotopy type of Spec(R) matches the homotopy 1-type of BO(\infty), the classifying space of the stable orthogonal group. This coincidence, I will argue, is the reason for "unitary" phenomena in physics. The second coincidence is a categorification of this: I will describe a setting in which Spec(R) has an "etale" homotopy type that matches the homotopy 2-type of BO(\infty), and explain how this provides the "spin--statistics theorem" relating spinors to fermions.