Tom Brown (mathematician) explained

Birth Name:	Thomas Craig Brown
Birth Place:	Portland, Oregon, U.S.
Alma Mater:	Reed College (BS) Washington University in St. Louis (Ph.D.)
Fields:	Mathematics Ramsey Theory
Work Institution:	Simon Fraser University
Doctoral Advisor:	Earl Edwin Lazerson
Thesis Title:	On Semigroups which are Unions of Periodic Groups
Thesis Year:	1964

Thomas Craig Brown (born 1938) is an American-Canadian mathematician, Ramsey Theorist, and Professor Emeritus at Simon Fraser University.^[1]

Collaborations

As a mathematician, Brown’s primary focus in his research is in the field of Ramsey Theory. When completing his Ph.D., his thesis was 'On Semigroups which are Unions of Periodic Groups'^[2] In 1963 as a graduate student, he showed that if the positive integers are finitely colored, then some color class is piece-wise syndetic.^[3]

In A Density Version of a Geometric Ramsey Theorem.^[4] he and Joe P. Buhler show that “for every

\varepsilon > 0 there is an n(\varepsilon) such that if n = dim(V) \geq n(\varepsilon) then any subset of V with more than \varepsilon|V| elements must contain 3 collinear points” where V is an n -dimensional affine space over the field with p ^{d} elements, and p ≠ 2 ".

In Descriptions of the characteristic sequence of an irrational,^[5] Brown discusses the following idea: Let

\alpha be a positive irrational real number. The characteristic sequence of \alpha is f(\alpha) = f _{1} f _{2} \ldots ; where f _{n} = [ ( n +1 )\alpha] [\alpha] .” From here he discusses “the various descriptions of the characteristic sequence of α which have appeared in the literature” and refines this description to “obtain a very simple derivation of an arithmetic expression for [n\alpha] .” He then gives some conclusions regarding the conditions for [n\alpha] which are equivalent to f _{n} = 1 .

He has collaborated with Paul Erdős, including Quasi-Progressions and Descending Waves^[6] and Quantitative Forms of a Theorem of Hilbert.^[7]

External links

• Archive of papers published by Tom Brown
• 2003 INTEGERS conference dedicated to Tom Brown

Notes and References

1. Web site: Tom Brown Professor Emeritus at SFU . 10 November 2020.
2. Book: Jensen . Gary R. . 150 Years of Mathematics at Washington University in St. Louis . Krantz . Steven G. . 2006 . American Mathematical Society . 978-0-8218-3603-3 . 15.
3. Brown . T. C. . An interesting combinatorial method in the theory of locally finite semigroups. . Pacific Journal of Mathematics . 1971 . 36 . 2 . 285–289 . 10.2140/pjm.1971.36.285 . free .
4. Brown . T. C. . Buhler . J. P. . A Density version of a Geometric Ramsey Theorem . . Series A . 1982 . 32 . 20–34 . 10.1016/0097-3165(82)90062-0 . free .
5. Brown . T. C. . Descriptions of the Characteristic Sequence of an Irrational. . . 1993 . 36 . 15–21 . 10.4153/CMB-1993-003-6 . free .
6. Brown . T. C. . Erdős . P. . Freedman . A. R. . Quasi-Progressions and Descending Waves . . Series A . 1990 . 53 . 81–95 . 10.1016/0097-3165(90)90021-N.
7. Brown . T. C. . Chung . F. R. K. . Erdős . P. . Quantitative Forms of a Theorem of Hilbert . . Series A . 1985 . 38 . 2 . 210–216 . 10.1016/0097-3165(85)90071-8 . free .