The main area of my research interests is the scale-invariance that appears in various problems of statistical physics. Thus when the length-scale of observation is changed by a factor then an identical object is recovered, at least statistically . The best known example of this in condensed matter area occurs at thermodynamic critical points such as the liquid- gas critical point.
Scale invariance occurs in abundance there.
This idea was expanded and supplemented to become the celebrated renormalization group theory of Kenneth Wilson. In fact in two dimensions these clusters are themselves scale-invariant directly in real space at the critical point. Mandelbrot coined the term fractal to describe these objects which are scale-invariant in real space, and their study is an important part of the research of scale invariance in statistical physics today. In addition, I am interested in the application of massively parallel computing to these areas. I have an on-going collaboration with some computer scientists in this pursuit, which already won us an international award called the Gordon Bell Prize in 1992.