Biography:Tom Brown (mathematician)
Tom Brown | |
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| Born | Thomas Craig Brown 1938 Portland, Oregon , U.S. |
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| Institutions | Simon Fraser University |
| Thesis | On Semigroups which are Unions of Periodic Groups (1964) |
| Doctoral advisor | Earl Edwin Lazerson |
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 [math]\displaystyle{ \varepsilon \gt 0 }[/math] there is an [math]\displaystyle{ n(\varepsilon) }[/math] such that if [math]\displaystyle{ n = dim(V) \geq n(\varepsilon) }[/math] then any subset of [math]\displaystyle{ V }[/math] with more than [math]\displaystyle{ \varepsilon|V| }[/math] elements must contain 3 collinear points” where [math]\displaystyle{ V }[/math] is an [math]\displaystyle{ n }[/math]-dimensional affine space over the field with [math]\displaystyle{ p^d }[/math] elements, and [math]\displaystyle{ p \neq 2 }[/math]".
In Descriptions of the characteristic sequence of an irrational,[5] Brown discusses the following idea: Let [math]\displaystyle{ \alpha }[/math] be a positive irrational real number. The characteristic sequence of [math]\displaystyle{ \alpha }[/math] is [math]\displaystyle{ f(\alpha) = f_1 f_2 \ldots }[/math]; where [math]\displaystyle{ f_n = [ ( n+1 )\alpha] [\alpha] }[/math].” 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 [math]\displaystyle{ [n\alpha] }[/math].” He then gives some conclusions regarding the conditions for [math]\displaystyle{ [n\alpha] }[/math] which are equivalent to [math]\displaystyle{ f_n = 1 }[/math].
He has collaborated with Paul Erdős, including Quasi-Progressions and Descending Waves[6] and Quantitative Forms of a Theorem of Hilbert.[7]
References
- ↑ "Tom Brown Professor Emeritus at SFU". https://www.sfu.ca/math/department/faculty/brown--tom.html. Retrieved 10 November 2020.
- ↑ Jensen, Gary R.; Krantz, Steven G. (2006). 150 Years of Mathematics at Washington University in St. Louis. American Mathematical Society. p. 15. ISBN 978-0-8218-3603-3. https://books.google.com/books?id=BZIbCAAAQBAJ.
- ↑ Brown, T. C. (1971). "An interesting combinatorial method in the theory of locally finite semigroups.". Pacific Journal of Mathematics 36 (2): 285–289. doi:10.2140/pjm.1971.36.285. http://people.math.sfu.ca/~vjungic/tbrown/tom-59.pdf.
- ↑ Brown, T. C.; Buhler, J. P. (1982). "A Density version of a Geometric Ramsey Theorem". Journal of Combinatorial Theory. Series A 32: 20–34. doi:10.1016/0097-3165(82)90062-0. http://people.math.sfu.ca/~vjungic/tbrown/tom-51.pdf.
- ↑ Brown, T. C. (1993). "Descriptions of the Characteristic Sequence of an Irrational.". Canadian Mathematical Bulletin 36: 15–21. doi:10.4153/CMB-1993-003-6. http://people.math.sfu.ca/~vjungic/tbrown/tom-31.pdf.
- ↑ Brown, T. C.; Erdős, P.; Freedman, A. R. (1990). "Quasi-Progressions and Descending Waves". Journal of Combinatorial Theory. Series A 53: 81–95. doi:10.1016/0097-3165(90)90021-N.
- ↑ Brown, T. C.; Chung, F. R. K.; Erdős, P. (1985). "Quantitative Forms of a Theorem of Hilbert". Journal of Combinatorial Theory. Series A 38 (2): 210–216. doi:10.1016/0097-3165(85)90071-8. http://people.math.sfu.ca/~vjungic/tbrown/tom-42.pdf.
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