Louis Christie lgc26@cam.ac.uk
New Zealand
Pure Mathematics and Mathematical Statistics, St Catharine's College
PhD thesis: Geometric Methods in Statistics
Research interests:
1. Manifold Statistics
2. Manifold Learning
3. Functional Data Analysis
My PhD focuses on the use of methods from differential geometry and functional analysis in statistical problems. Many types of data are constrained in some way. In these constrained spaces the usual linear techniques can produce weird and unusual results because they ignore the geometry, the true special structure, of these spaces. If we can include this information we can often produce more accurate and precise estimates, more powerful statistical tests, and often more insight into the underlying problem. I will be working to understand the statistical properties of some new tools that use this geometric information. These tools have applications in diverse areas such as neuroimaging, speech analysis, and machine learning.
Who or what inspired you to pursue your research interests?
I was originally inspired to pursue mathematics in high school when I participated in the New Zealand Mathematical Olympiad training programme. It showed me how mathematics is about more than just calculations – it is about the structure of problems and how to develop methods to solve them. I’ve always found spatial and geometric problems the most interesting, and am excited to use the mathematical tools I’ve worked on in these areas to new statistical problems.