Greg Kuperberg

Regular Faculty
Topology and combinatorics
Ph.D., 1991, University of California, Berkeley
Refereed publications: Via Math Reviews

Web Page:
Office: MSB 2216
Current Courses: MAT 21C
Office Hours: T 2pm-3pm


I do research in various areas of mathematics, including quantum algebra, quantum probability and computation, geometric topology, combinatorics, and convex geometry. The word "quantum" in the sense of my research means non-commutative generalizations of mathematical objects that are usually described by commutative algebras. Quantum probability is the study of non-commutative algebras and random variables, quantum groups are like Lie groups but with non-commuting coordinates, etc. I also have non-quantum results and interests in geometry and combinatorics, some of them inspired by quantum mathematics.

Selected Publications

    [1] G. Kuperberg, "Knottedness is in NP, modulo GRH," preprint, 2011. arXiv:1112.0845,

    [2] G. Kuperberg, "How hard it it to approximate the Jones polynomial," to appear in Theory Comput, 84: 83-129, 1996. arXiv:0908.0512.

    [3] G. Kuperberg, "From the Mahler conjecture to Gauss linking integrals," Geom. Funct. Anal., 18(3):870-892, 2008. Full Text, arXiv:math/0610904, MR 2438998.

    [4] G. Kuperberg, "A subexponential-time quantum algorithm for the dihedral hidden subgroup problem," SIAM J. Comput., 35(1):170-188, 2005. Full Text, arXiv:quant-ph/0302112, MR2178804.

    [5] G. Kuperberg, "Symmetry classes of alternating-sign matrices under one roof," Ann. of Math. (2) 156 (3): 835-866, 2002. Full Text, arXiv:math/0008184, MR1954236.

Honors and Awards

NSF Postdoctoral Fellowship, 1991-1994
Sloan Foundation Research Fellowship, 1998


Dongseok Kim (2003), Chris Bumgardner (2010), Sonya Berg (2012), Rohit Thomas, Stephen Lu.

Last updated: 2012-04-14