Joe Peter Buhler (born 1950 in

Vancouver, Washington Vancouver ( ) is a city on the north bank of the Columbia River in the U.S. state of Washington (state), Washington, located in Clark County, Washington, Clark County. Founded in 1825 and incorporated in 1857, Vancouver had a population of 190, ...

) is an American mathematician known for his contributions to

algebraic number theory Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic ob ...

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

and

cryptography Cryptography, or cryptology (from "hidden, secret"; and ''graphein'', "to write", or ''-logy, -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of Adversary (cryptography), ...

Education and career

Buhler received his undergraduate degree from

Reed College Reed College is a Private college, private Liberal arts colleges in the United States, liberal arts college in Portland, Oregon, United States. Founded in 1908, Reed is a residential college with a campus in the Eastmoreland, Portland, Oregon, E ...

in 1972, and his Ph.D. from

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

in 1977 with thesis ''Icosahedral Galois Representations'' and thesis advisor John Tate. Buhler was a professor at Reed College in

Portland, Oregon Portland ( ) is the List of cities in Oregon, most populous city in the U.S. state of Oregon, located in the Pacific Northwest region. Situated close to northwest Oregon at the confluence of the Willamette River, Willamette and Columbia River, ...

from 1980 until his retirement in 2005. From 2004 to 2017, he was director of the IDA Center for Communications Research in La Jolla, California. In 1997, he introduced, with

Zinovy Reichstein Zinovy Reichstein (born 1961) is a Russian-born American mathematician. He is a professor at the University of British Columbia in Vancouver. He studies mainly algebra, algebraic geometry and algebraic groups. He introduced (with Joe P. Buhler) th ...

, the concept of essential dimension. 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 was ...

of Harry Vandiver and

Ernst Eduard Kummer Ernst Eduard Kummer (29 January 1810 – 14 May 1893) was a German mathematician. Skilled in applied mathematics, Kummer trained German army officers in ballistics; afterwards, he taught for 10 years in a '' gymnasium'', the German equivalent of h ...

concerning the class number of

cyclotomic field In algebraic number theory, a cyclotomic field is a number field obtained by adjoining a complex root of unity to \Q, the field of rational numbers. Cyclotomic fields played a crucial role in the development of modern algebra and number theory ...

s. 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. 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.

References

External links

Homepage

photo and biography on the occasion of a lecture

author's profile
in the database

zbMATH zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastru ...

{{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