Joe Peter Buhler (born 1950 in Vancouver, Washington) is an American mathematician known for his contributions to algebraic number theory, algebra and cryptography.
Education and career[edit]
Buhler received his undergraduate degree from Reed College in 1972, and his Ph.D. from Harvard University in 1977 with thesis Icosahedral Galois Representations and thesis advisor John Tate.[1][2] Buhler was a professor at Reed College in Portland, Oregon from 1980 until his retirement in 2005.[3] From 2004 to 2017, he was director of the IDA Center for Communications Research in La Jolla, California.[4]
In 1997, he introduced, with Zinovy Reichstein, the concept of essential dimension.[5]
Buhler is involved in a project to numerically verify the Kummer–Vandiver conjecture of Harry Vandiver and Ernst Eduard Kummer concerning the class number of cyclotomic fields. Vandiver proved it with a desk calculator up to class number 600, Derrick Lehmer (in the late 1940s) to about 5000, and Buhler with colleagues (in 2001) to 12 million.[6] He continues the project with David Harvey and others.[7]
He was elected a Fellow of the American Mathematical Society in 2012.
References[edit]
- ^ Joe Peter Buhler at the Mathematics Genealogy Project
- ^ Buhler, Joe P. (1978). Icosahedral Galois Representations. Lecture Notes in Mathematics 654. Springer Verlag. Buhler, J. P (2006-11-15). 2006 pbk reprint. ISBN 9783540358183.
- ^ Reed College, Emeriti
- ^ Buhler, Joe; Graham, Ron; Hales, Al (2018). ""Maximally nontransitive dice"". American Mathematical Monthly. 125 (5): 387–399. doi:10.1080/00029890.2018.1427392.
- ^ Buhler, JP; Reichstein, Z. (1997). "On the essential dimension of a finite group". Compositio Mathematica. 106 (2): 159–179. doi:10.1023/A:1000144403695.
- ^ J. P. Buhler, Richard Crandall, Reijo Ernvall, Tauno Metsänkylä, M. Amin Shokrollahi Irregular primes and cyclotomic invariants to 12 million, Journal of Symbolic Computation, Vol. 31, 2001, pp. 89–96 doi:10.1006/jsco.1999.1011
- ^ Buhler, J.P.; Harvey, D. (2009). "Irregular primes up to 163 million". arXiv:0912.2121 [math.NT].
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