mathematics

Greg Kuperberg

Greg Kuperberg is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Greg Kuperberg rather than just read about it. In short: Greg Kuperberg (born July 4, 1967) is a Polish-born American mathematician known for his contributions to geometric topology, quantum algebra, and combinatorics. Kuperberg is a professor of mathematics at the University of California, Davis.

Key takeaways

Greg Kuperberg belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Greg Kuperberg to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Greg Kuperberg from memory before moving on to harder problems.

Reference excerpt

Greg Kuperberg (born July 4, 1967) is a Polish-born American mathematician known for his contributions to geometric topology, quantum algebra, and combinatorics. Kuperberg is a professor of mathematics at the University of California, Davis.

Biography Kuperberg is the son of two mathematicians, Krystyna Kuperberg and Włodzimierz Kuperberg. He was born in Poland in 1967, but his family emigrated to Sweden in 1969 due to the 1968 Polish political crisis. In 1972, Kuperberg's family moved to the United States, eventually settling in Auburn, Alabama. Kuperberg wrote three computer games for the IBM Personal Computer in 1982 and 1983 (which were published by Orion Software): Paratrooper, PC-Man and J-Bird. (video game clones of Sabotage, Pac-Man and Q*bert, respectively) He enrolled at Harvard University in 1983 and received a bachelor's degree in 1987. He was ranked Top 10 in the 1986 William Lowell Putnam Mathematical Competition. Upon leaving Harvard, Kuperberg studied at the University of California, Berkeley under Andrew Casson, receiving a Ph.D. in geometric topology and quantum algebra in 1991. From 1991 until 1992, Kuperberg was a NSF postdoctoral fellow and adjunct assistant professor at Berkeley, and from 1992 to 1995 held a Dickson Instructorship at the University of Chicago. From 1995 through 1996, Kuperberg was Gibbs Assistant Professor at Yale University after which he joined the mathematics faculty at the University of California, Davis. In 2012 he became a fellow of the American Mathematical Society. Kuperberg is married to physicist Rena Zieve, who is a professor of physics at UC Davis.

Selected publications Kuperberg has over fifty publications, including two in the Annals of Mathematics.

Kuperberg, Greg (1994). "The quantum G2 link invariant". International Journal of Mathematics. 5 (1): 61–85. arXiv:math/9201302. doi:10.1142/S0129167X94000048. Kuperberg, Greg (1996). "Non-involutory Hopf algebras and 3-manifold invariants". Duke Mathematical Journal. 84: 83–129. arXiv:q-alg/9712047. doi:10.1215/S0012-7094-96-08403-3. S2CID 15086645. with Krystyna Kuperberg: Kuperberg, Greg; Kuperberg, Krystyna (1996). "Generalized counterexamples to the Seifert conjecture". Annals of Mathematics. Second Series. 144 (3): 547–576. arXiv:math/9802040. doi:10.2307/2118536. JSTOR 2118536. S2CID 16309410. Kuperberg, Greg (2002). "Symmetry classes of alternating-sign matrices under one roof". Annals of Mathematics. Second Series. 156 (3): 835–866. arXiv:math/0008184. doi:10.2307/3597283. JSTOR 3597283. S2CID 7965653. Kuperberg, Greg (2005). "A subexponential-time quantum algorithm for the dihedral hidden subgroup problem". SIAM Journal on Computing. 35 (1): 170–188. arXiv:quant-ph/0302112. doi:10.1137/S0097539703436345. S2CID 15965140. Kuperberg, Greg (2006). "Numerical cubature using error-correcting codes". SIAM Journal on Numerical Analysis. 44 (3): 897–907. arXiv:math/0402047. doi:10.1137/040615572. S2CID 18689951. Kuperberg, Greg (1 May 2014), "Knottedness is in NP, modulo GRH", Advances in Mathematics, 256: 493–506, doi:10.1016/j.aim.2014.01.007

References

External links Greg Kuperberg, faculty page at UC-Davis Greg Kuperberg at the Mathematics Genealogy Project Bits from my personal collection - the original IBM PC and Orion Software 2025 Interview with Greg Kuperberg

Illustrations

Worked examples

Example 1 — a first encounter with Greg Kuperberg

Start with the simplest possible case. Write down what Greg Kuperberg claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Greg Kuperberg before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Greg Kuperberg ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Greg Kuperberg

In research: Greg Kuperberg appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Greg Kuperberg in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Greg Kuperberg is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1967 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Greg Kuperberg outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Greg Kuperberg in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Greg Kuperberg means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Greg Kuperberg out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Greg Kuperberg in simple terms?

Why does Greg Kuperberg matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Greg Kuperberg?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Greg Kuperberg.