Quantum Topology / Hopf Algebra Seminar
Greg Kuperberg
UC Davis
How hard is it to approximate the Jones polynomial?
Abstract: The short answer is that it's #P-hard. The longer answer
is that it was an algorithm was constructed in the quantum computation
community to approximate the Jones polynomial at a principal root of
unity, except with a diagram-dependent normalization factor. I will
present my result that if you strip away this normalization factor to
ask for any fair approximation, then approximating the Jones
polynomial is as hard as any combinatorial counting problem and almost
certainly out of reach for classical or even quantum computers. It
is conjectured that the Jones polynomial distinguishes the unknot, but
we can envision that we can know whether a complicated knot diagram is
an unknot long before we know much about its Jones polynomial.
Thursday September 17, 2015 at 3:00 PM in SEO 612