Tom Brown (mathematician)

Thomas Craig Brown (born 1938) 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 $\epsilon >0$ there is an $n(\epsilon )$ such that if $n=dim(V)\ge n(\epsilon )$ then any subset of $V$ with more than $\epsilon |V|$ elements must contain 3 collinear points” where $V$ is an $n$-dimensional affine space over the field with $p^d$ elements, and $p\ne 2$".

In Descriptions of the characteristic sequence of an irrational, Brown discusses the following idea: Let $\alpha$ be a positive irrational real number. The characteristic sequence of $\alpha$ is $f(\alpha )=f_1{f}_2\dots$; 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 and Quantitative Forms of a Theorem of Hilbert.

External links

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