Tom Brown (mathematician)

Thomas Craig Brown is an American-Canadian mathematician, Ramsey Theorist, and Professor Emeritus at Simon Fraser University.

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' In 1963 as a graduate student, he showed that if the positive integers are finitely colored, then some color class is piece-wise syndetic.
In A Density Version of a Geometric Ramsey Theorem, he and Joe P. Buhler showed 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, 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 and Quantitative Forms of a Theorem of Hilbert.