367 citations · 1.6k across the 63 of their papers we have counts for
69 papers
Odd Vassiliev invariants vanish at four loops
Greg Kuperberg
The odd Vassiliev conjecture asserts that all Jacobi diagrams with an odd number of legs vanish modulo the AS and IHX relations. Equivalently, the conjecture asserts that Vassiliev…
Breaking the cubic barrier in the Solovay-Kitaev algorithm
Greg Kuperberg
We improve the Solovay--Kitaev theorem and algorithm for a general finite, inverse-closed generating set acting on a qudit. Prior versions of the algorithm efficiently find a word…
Coloring invariants of knots and links are often intractable
Greg Kuperberg, Eric Samperton
Let be a nonabelian, simple group with a nontrivial conjugacy class . Let be a diagram of an oriented knot in , thought of as computational input. We sh…
On TQFT representations of mapping class groups with boundary
Greg Kuperberg, Shuang Ming
We study the TQFT mapping class group representations for surfaces with boundary associated with the gauge group, or equivalently the quantum group $U_q(\Sl(2))$. We show t…
Computational complexity and 3-manifolds and zombies
Greg Kuperberg, Eric Samperton
We show the problem of counting homomorphisms from the fundamental group of a homology -sphere to a finite, non-abelian simple group is #P-complete, in the case that …
The Computational Complexity of Ball Permutations
Scott Aaronson, Adam Bouland, Greg Kuperberg +1
Inspired by connections to two dimensional quantum theory, we define several models of computation based on permuting distinguishable particles (which we call balls), and character…