# Greg Kuperberg

**Home Page: ** http://www.math.ucdavis.edu/~greg/**Year joining UC Davis:** 1996**Degree:** Ph.D., 1991, University of California, Berkeley**Refereed publications:** Via Math Reviews

### Research

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

- G. Kuperberg, "Knottedness is in NP, modulo GRH," preprint, 2011.
arXiv:1112.0845,
- G. Kuperberg, "How hard it it to approximate the Jones polynomial," to appear in
*Theory Comput*,**84**: 83-129, 1996. arXiv:0908.0512. - 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. - 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. - 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

### Students

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

*Last updated: 2012-04-14*