# Greg Kuperberg

Gregory John " Greg" Kuperberg ( born July 4, 1967 in Gdansk, Poland) is an American mathematician.

He is the son of mathematician Krystyna Kuperberg and Włodzimierz Kuperberg, a professor at Auburn University, and came with his parents to Sweden in 1969 and 1972 in the USA to Auburn ( Alabama). 1982/88 he was a game programmer for the company Orion (including Paratrooper ). He has already visited from 1979 Mathematics courses at Auburn University, where his parents taught, and Oklahoma State University, where his mother taught. From 1983, he studied at Harvard University with a bachelor's degree magna cum laude in 1987 and 1991, he received his doctorate at the University of California, Berkeley, with Andrew Casson ( Invariants of links and 3- manifolds via multilinear algebra and Hopf Algebras ) .. After that, he was adjunct assistant professor at Berkeley until 1995 Dickson Instructor at the University of Chicago in 1992 and 1995/96 Gibbs Assistant Professor at Yale University. He was an Assistant Professor, Associate Professor in 1997 and 2001, a professor at the University of California, Davis in 1996.

It deals with geometric topology, Quantenalgebren, combinatorics, convex geometry, but also quantum information theory and numerical mathematics. In 2002, he gave an alternative proof of the Alternating Sign Matrix conjecture, which was proved by Doron Zeilberger first. In 2011 he proved under the assumption of the generalized Riemann conjecture that the problem whether a node diagram illustrates the trivial knot is NP-hard. With his mother Krystyna Kuperberg, he published over generalized counter-examples to the Seifert conjecture (his mother was 1993, the first smooth counterexample ).

2004/ 05 he was a visiting professor at Cornell University and 2010/11 at the University of Grenoble.

In 2012 he became a Fellow of the American Mathematical Society. He was twice a Sloan Fellow and received the 1990 Prize Morrey, Berkeley.

He is married to the solid-state physicists Ziewe Rena, who is also a professor at the University of California, Davis.

## Writings

- Noam Elkies, Michael Larsen, James Propp: Alternating -sign matrices and domino tilings. I. J. Algebraic Combin. 1 (1992 ), no 2, 111-132. II ibid., no 3, 219-234.
- The quantum G2 link invariant, Internat. J. Math, Vol 5, 1994, pp. 61-85.
- Another proof of the alternating -sign matrix conjecture. Boarding. Math Res Notices 1996, no 3, 139-150.
- Non- involutory Hopf algebras and 3 -manifold invariants, Duke Math J., Vol 84, 1996, pp. 83-129.
- Spiders for rank 2 Lie algebras. Comm. Math Phys. 180 (1996), no 1, 109-151.
- With Krystyna Kuperberg Generalized counterexamples to the Seifert conjecture, Annals of Mathematics, Volume 144, 1996, pp. 547-576.
- Symmetry classes of alternating -sign matrices under one roof, Annals of Mathematics, Volume 156, 2002, pp. 835-866.
- A subexponential -time quantum algorithm for the dihedral hidden subgroup problem-, SIAM J. Comput. 35 (2005 ), no 1, 170-188. arxiv 2003
- Numerical cubature using error -correcting codes, SIAM J. Numer. Anal. 44 (2006 ), no 3, 897-907. arxiv 2004
- Knottedness is in NP, modulo GRH. arxiv 2011