# Greg Kuperberg

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, 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

- G. Kuperberg, "Knottedness is in NP, modulo GRH,"
*Adv. Math.***256**:493-506, 2014. arXiv:1112.0845, - G. Kuperberg, "How hard it it to approximate the Jones polynomial?",
*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. arXiv:math/0610904. - 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. - 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.

### Students

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*