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Tuesday, September 17, 2019

**Abstract:** I’ll give an overview of my result with Greg Kuperberg concerning the computational complexity of G-coloring invariants of knots, where G is a finite, simple group. We have a similar theorem for closed 3-manifolds. I’ll try to give a sense of the commonalities of the two proofs (e.g. “reversible computing with a combinatorial TQFT”), as well as where they differ (there’s some interesting algebraic topology that needed developing in the knot case). Time permitting, I’ll discuss the special case of hyperbolic knots and 3-manifolds.