Ellis Kolchin

Ellis Robert Kolchin (April 18, 1916 – October 30, 1991) was an American mathematician at Columbia University. He earned a doctorate in mathematics from Columbia University in 1941 under supervision of Joseph Ritt. Shortly after he served in the South Pacific in World War II. He was awarded a Guggenheim Fellowship in 1954 and 1961.

Ellis Kolchin
Born	(1916-04-18)April 18, 1916 New York City, U.S.
Died	October 30, 1991(1991-10-30) (aged 75) New York City, U.S.
Alma mater	Columbia University
Known for	Lie–Kolchin theorem Kolchin topology
Scientific career
Fields	Mathematics
Institutions	Columbia University
Doctoral advisor	Joseph Ritt
Doctoral students	Azriel Rosenfeld Irving Adler Alexandru Buium

Kolchin worked on differential algebra and its relation to differential equations, and founded the modern theory of linear algebraic groups. He developed many of the basic theorems including an analog of the Hilbert Basis Theorem further developing the Galois Theory of Differential Equations started by Liouville. He is an celebrated figure in Differential Algebra and his book Differential Algebra and Algebraic Groups has been extremely influential in Differential Algebra, Model Theory and Beyond.

In a book review Blum writes: This book, published after years of careful preparation, is a tour de force of the highest proportions. The author, as is well known, is the leading authority in the field of differential algebra. There are few people working in this area who have not benefited enormously through personal contact with him and none who have not been influenced by his publications. His goal here is to present a unified exposition of the subject, in an algebraic setting, presuming no more than a standard first year graduate course in algebra.

He gave a famous plenary address at the International Congress of Mathematicians in 1966 (Moscow) where he outlined Kolchin's problems a famous collection of unsolved problems in Differential Algebra.

His seminar in differential algebra, the Kolchin Seminar, was the longest ongoing mathematics seminar at Columbia University, ran for over 30 years. It is currently run by the City University of New York.

His doctoral students include Azriel Rosenfeld, Irving Adler, and (unofficially) Alexandru Buium.

See also

• Kolchin topology
• Lie–Kolchin theorem
• Picard–Vessiot theory
• Kolchin-Schmidt Conjecture
• Jacobi Bound Conjecture
• Ritt Problem
• Kolchin Catenary Conjecture

Publications

• Kolchin, E. R. (1985), Differential algebraic groups, Pure and Applied Mathematics, vol. 114, Boston, MA: Academic Press, ISBN 978-0-12-417640-9, MR 0776230
• Kolchin, E. R. (1973), Differential algebra and algebraic groups, Pure and Applied Mathematics, vol. 54, Boston, MA: Academic Press, ISBN 978-0-12-417650-8, MR 0568864
• Kolchin, Ellis (1999), Selected works of Ellis Kolchin with commentary, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-0542-8, MR 1677530

References

• Bass, Hyman; Cassidy, Phyllis J.; Kovacic, Jerald, eds. (1977), Contributions to algebra, A collection of papers dedicated to Ellis Kolchin, New York: Academic Press [Harcourt Brace Jovanovich Publishers], ISBN 978-0-12-080550-1, MR 0457031
• Bass, Hyman; Cassidy, Phyllis (1992), "Ellis Kolchin (1916--1991)", Notices of the American Mathematical Society, 39 (6): 599–600, ISSN 0002-9920, MR 1170740
• Borel, Armand (2001), Essays in the history of Lie groups and algebraic groups, History of Mathematics, vol. 21, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-0288-5, MR 1847105
• Hevesi, Dennis (November 3, 1991), "Prof. Ellis R. Kolchin Dies at 75; A Shaper of Differential Algebra", New York Times Obituary
• O'Connor, John J.; Robertson, Edmund F., "Ellis Kolchin", MacTutor History of Mathematics Archive, University of St Andrews

External links

• Ellis Kolchin at the Mathematics Genealogy Project