turkmath.org

Deligne's work on Tannakian duality identifies the category sVec of super vector spaces as the "algebraic closure" of the category Vec of vector spaces (over $\mathbb C$). I will describe my construction, joint with David Reutter, of the higher-categorical analog of sVec: the algebraic closure of the n-category of "n-vector spaces". The construction mixes ideas from Galois theory, quantum physics, homotopy theory, and fusion category theory. Time permitting, I will describe the higher-categorical Galois group, which turns out to have a surgery-theoretic description through which it is almost, but not quite, the group PL.