General Profile


Greg Kuperberg

Topology and combinatorics
Ph.D., 1991, University of California, Berkeley

Web Page:
Office: MSB 2216
Current Courses: MAT 127C
Office Hours: MWF 2pm-2:30pm


I do research in various areas of mathematics, including quantum algebra, quantum probability, quantum computing, 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," Adv. Math. 256:493-506, 2014. arXiv:1112.0845,
  2. G. Kuperberg, "How hard it it to approximate the Jones polynomial?", 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. arXiv:math/0610904.
  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.
  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.

Honors and Awards

  • NSF Postdoctoral Fellowship in Mathematics, 1991.
  • Sloan Foundation Research Fellowship, 1998.
  • Fellow of the American Mathematical Society, 2012.


Dongseok Kim (2003), Chris Bumgardner (2011), Sonya Berg (2012), Rohit Thomas (2012), Stephen Lu (2014), Eric Samperton (2018), Colin Hagemeyer (2018), Shuang Ming (2019), Nate Gallup, Robert Sanders.

Last updated: 2019-09-13