367 citations · 1.6k across the 63 of their papers we have counts for
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Scholarly mathematical communication at a crossroads
Greg Kuperberg
This essay was invited for publication in Nieuw Archief voor Wiskunde; it will also appear in translation in the SMF Gazette and in the DMV Mitteilungen. I discuss the recent trend…
Finite, connected, semisimple, rigid tensor categories are linear
Greg Kuperberg
Fusion categories are fundamental objects in quantum algebra, but their definition is narrow in some respects. By definition a fusion category must be k-linear for some field k, an…
What is a virtual link?
Greg Kuperberg
Several authors have recently studied virtual knots and links because they admit invariants arising from R-matrices. We prove that every virtual link is uniquely represented by a l…
Fat 4-polytopes and fatter 3-spheres
David Eppstein, Greg Kuperberg, Günter M. Ziegler
We introduce the fatness parameter of a 4-dimensional polytope P, defined as ϕ(P)=(f_1+f_2)/(f_0+f_3). It arises in an important open problem in 4-dimensional combinatorial geometr…
The Second Hull of a Knotted Curve
Jason Cantarella, Greg Kuperberg, Rob Kusner +1
The convex hull of a set K in space consists of points which are, in a certain sense, "surrounded" by K. When K is a closed curve, we define its higher hulls, consisting of points…
The capacity of hybrid quantum memory
Greg Kuperberg
The general stable quantum memory unit is a hybrid consisting of a classical digit with a quantum digit (qudit) assigned to each classical state. The shape of the memory is the vec…
A tracial quantum central limit theorem
Greg Kuperberg
We prove a central limit theorem for non-commutative random variables in a von Neumann algebra with a tracial state: Any non-commutative polynomial of averages of i.i.d. samples co…