Joe P. Buhler
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Joe Peter Buhler (born 1950 in Vancouver, Washington) is an American mathematician. Buhler received his undergraduate degree from Reed College in 1972, and his Ph.D. from
Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...
in 1977 with thesis ''Icosahedral Galois Representations'' and thesis advisor
John Tate John Tate may refer to: * John Tate (mathematician) (1925–2019), American mathematician * John Torrence Tate Sr. (1889–1950), American physicist * John Tate (Australian politician) (1895–1977) * John Tate (actor) (1915–1979), Australian act ...
. Buhler was a professor at Reed College in
Portland, Oregon Portland (, ) is a port city in the Pacific Northwest and the largest city in the U.S. state of Oregon. Situated at the confluence of the Willamette and Columbia rivers, Portland is the county seat of Multnomah County, the most populous co ...
from 1980 until his retirement in 2005. In 1997, he introduced, with Zinovy Reichstein, the concept of
essential dimension In mathematics, essential dimension is an invariant (mathematics), invariant defined for certain algebraic structures such as algebraic groups and quadratic forms. It was introduced by Joe P. Buhler, J. Buhler and Zinovy Reichstein, Z. Reichstein an ...
. Buhler is involved in a project to numerically verify the
Kummer–Vandiver conjecture In mathematics, the Kummer–Vandiver conjecture, or Vandiver conjecture, states that a prime ''p'' does not divide the class number ''hK'' of the maximal real subfield K=\mathbb(\zeta_p)^+ of the ''p''-th cyclotomic field. The conjecture wa ...
of
Harry Vandiver Harry Schultz Vandiver (21 October 1882 – 9 January 1973) was an American mathematician, known for work in number theory. He was born in Philadelphia, Pennsylvania to John Lyon and Ida Frances (Everett) Vandiver. He did not complete a form ...
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. He continues the project with David Harvey and others. Buhler's research deals with algorithmic algebraic number theory, algebra, and
cryptography Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adver ...
. He was elected a Fellow of the
American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
in 2012.


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External links


Homepage

photo and biography on the occasion of a lecture

author's profile
in the database zbMATH {{DEFAULTSORT:Buhler, Joe P. 20th-century American mathematicians 21st-century American mathematicians Reed College alumni Harvard University alumni Reed College faculty Fellows of the American Mathematical Society 1950 births Living people People from Vancouver, Washington