Welcome to my page. I have an Honorary Research Fellowship in the Department of Mathematics at La Trobe University since June 2003. I have always worked full time in a career outside of university; even whilst doing my PhD at ANU in 1996-97 under Professor Rodney J Baxter. Apart from my Graduate Diploma in 2001, I have never taken time away from work for study or research. My main academic interest and publication has been mathematics. Although I consider myself a Number Theorist, much that I have published has been applicable to Statistical Mechanics and other areas of Theoretical Physics. However, I have also published poetry in literary magazines and have academic contacts there too.

In a recent development, I have found that my analogues for q-series contain functions as coefficients that enumerate tiling patterns found in the Theory of Quasicrystals. An example of such a tiling pattern is:-

I have a mathematics homepage of greater detail at http://www.geocities.com/qseriesgeoff/ , and a poetry homepage at http://www.geocities.com/geoffreycampbell/. Some examples of my research papers are here:- An Euler product transform applied to q-series (PDF file) , Dirichlet series analogues of q-shifted factorial and the q-Kummer sum (PDF file) and The Ramanujan trigonometric function and visible point identities (PDF file).  My full list of maths research papers I wrote is at http://www.geocities.com/qseriesgeoff/vpv2.html .

Much of my published work is quite easily understood by undergraduates. For example, the countable set of fractions between zero and one can be depicted as

or they can be drawn as the coordinates of the visible lattice points (ie those whose coordinates are relatively prime) as follows

The dots in this diagram are the visible from the origin points, and the crosses are the so-called invisible points. The density of the dots in this depiction is .

These ideas apply to my identities I found

Particular cases of these are examined in some of my papers, where they are shown to have non-trivial simple cases. If each of the variables in the above identities are set equal to z, then the binomial coefficients appear as exponents in the right sides. An example of such an identity is

These identities interpret a fundamental property of n-dimensional Euclidean space, namely