# Greg Kuperberg

**Regular Faculty****Topology and combinatorics**

Ph.D., 1991, University of California, Berkeley**Refereed publications:** Via Math Reviews

**Web Page: ** http://www.math.ucdavis.edu/~greg/

Email: greg@math.ucdavis.edu

Office: MSB 2216

### 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

**[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

### Students

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

*Last updated: 2012-04-14*