Tom Brown | |
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Born | Thomas Craig Brown 1938 (age 85–86) 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]
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 there is an such that if then any subset of with more than elements must contain 3 collinear points” where is an -dimensional affine space over the field with elements, and ".
In Descriptions of the characteristic sequence of an irrational,[5] Brown discusses the following idea: Let be a positive irrational real number. The characteristic sequence of is ; where .” 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 .” He then gives some conclusions regarding the conditions for which are equivalent to .
He has collaborated with Paul Erdős, including Quasi-Progressions and Descending Waves[6] and Quantitative Forms of a Theorem of Hilbert.[7]