Symmetry Colloquia – Global Categorical Symmetries: The universal target category


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May 2, 2024 4:30 pm - 5:20 pm
CMSA, 20 Garden St, G10
Address: 20 Garden Street, Cambridge, MA 02138

Theo Johnson-Freyd - Dalhousie University and Perimeter Institute

Hilbert’s Nullstellensatz says that the complex numbers C satisfy a universal property among all R-algebras: every not-too-large nonzero commutative R-algebra maps to C. Deligne proved a similar statement in categorical dimension 1: every not-too-large symmetric monoidal category over R maps to the category sVec of super vector spaces. In other words, sVec (and not Vec!) is “algebraically closed”. These statements help explain why quantum field theory requires imaginary numbers and fermions. I will describe the universal symmetric monoidal higher category that extends the sequence C, sVec, …. This is joint work in progress with David Reutter, and builds on closely-related work by GCS collaborators Freed, Scheimbauer, and Teleman and Schlank et al.