I am a PhD student in the Applied Mathematics department, under the supervision of Prof. Edward Vrscay.
I previously did my MMath in Statistics (thesis option) under the supervision of Prof. Yi Shen. My thesis generalized his work in intrinsic location functionals to consider multiple locations at once.
My research interests are now contained somewhere in the intersection of fractal geometry, iterated function systems, and probability.
I am currently (as of early 2020) working on the problem of approximating real-valued data of arbitrary (finite) dimension with a function generated by finitely-many iterations of a fitted IFSM (iterated function system on maps), using a novel multiplicative error function which accounts for the inherent self-similarity of the fitting procedure.
My hope is that this work can be extended to vector-valued and spatial data; particularly data from ecological systems. I'd also like to contribute to a new 'language' of fractals wherein abstract fractal frameworks can be explored, modelled and analyzed - such as a functional model of human consciousness in relation to the self-similar function of the brain; a theory of ecological sustainability that exploits the self-similar structure of natural systems in a vein similar to permaculture; the psychology of learning, social media trends, propaganda campaigns; the connections to machine learning and artificial intelligence etc.
As such, I am always open to hearing about research in various fields where fractals are considered. While our research may be focused and specific, it's always a good idea to attempt to share a common language surrounding these questions.
