Contact Information

Research Information

Research Description

I study a primitive geometrical notion called `manifold theory.' In manifold theory we study various notions of `space.' Manifolds are the setting for the study of cosmology via the General Theory of Relativity. They also provide a framework for studying a seemingly simpler question: take a piece of string, tangle it up and glue the loose ends together. This is a jumbled loop of string. Can you determine (provably so) that this loop can or can not be untangled? Can you write a computer program that is guaranteed to determine the answer in a short amount of time? Those are the kinds of early questions that motivated the field -- the development of a mathematics for precise, yet non-quantitative, geometrical yet non-rigid problems. Topology has evolved significantly since its early years and now is used to develop robots capable of complex tasks, as well as statisticians to understand the large-scale structure of huge high-dimensional data-sets.

Research Keywords

International Involvement

Countries lived/worked in

Australia, France, Germany, United States, Singapore

Software Development

I write various software packages to aid in computation. The most substantial package that I contribute to is called Regina: http://regina.sourceforge.net/