Sina Greenwood
From MathsDept
Bio and Research - Publications - Supervision
Contents |
Topology
My primary field of research is topology and I mostly work collaboratively with colleagues/friends from other parts of the world. Much of my current work is in the following areas:
Generalised Inverse Limits
This is a relatively new area of research. A great deal is known about inverse limits, and they have been applied within fields as diverse as physics and economics. A generalised inverse limit is obtained by allowing the bonding functions to be upper semicontinuous set-valued functions. It turns out at many of the results for inverse limits, fail for generalised inverse limits. One such example, and the one that I have been particularly interested in addressing, is that every inverse limit is a continuum. I am collaborating with Judy Kennedy (Texas).
Discrete Dynamical Systems
Emerging from the classical fixed point theorems is the question: given a set with a self map, is it possible to endow the set with a topology satisfying some specified properties such that the self map is continuous. I have worked with several people on this question; Chris Good (Birmingham), Stephen Watson (Toronto), Robin Knight (Oxford), David McIntyre (Auckland) and more recently Aisling McCluskey (Galway) and Brian Raines (Texas).
The Advancement of Māori and Pasifika Students
I am of Samoan descent and have been involved in programmes designed to increase the recruitment and success of Māori and Pasifika university students in mathematics. In order to improve the efficacy of these programmes, I have embarked on a number of research projects. One was a longitudinal study tracking Māori students through high school in order to examine the factors that influence their decision to continue, or not, in mathematics. Another involved a collaboration with researchers at the National University of Samoa, looking at cultural factors that impact on effective learning in mathematics. My Auckland colleagues are Colleen McMurchy-Pilkington, Hannah Bartholomew and Louise Sheryn.
