Nathan Kirk

Current research project

Uniform Distribution in Compact Topological Groups with Application to Quasi-Monte Carlo Integration.

With a background in group theory, my advisor Dr Pausinger suggested that we consider looking at sequences in compact topological groups which possess a certain property. In particular, sequences which are uniformly distributed in these topological groups.

The theory of uniform distribution in the classical setting is concerned with the irregularity of the distribution of sequences of real numbers in the d-dimensional unit cube. This, along with theoretical abstract concepts and results for general spaces (such as compact Hausdorff spaces) are very well understood. However, despite this there are no concrete constructions of uniformly distributed sequences in abstract spaces.

Therefore, I plan to develop explicitly construct uniformly distributed sequences in compact groups and arrive at specific examples in order that I may implement these computationally (using Python) in quasi-Monte Carlo methods to allow approximation of numerical integrals defined over these groups.

Biography

I joined Queen’s University Belfast in 2015 on the BSc Mathematics course. Immediately I warmed to pure mathematics and made this area the focus of my study both in Queen’s and in The University of St Andrews where I studied my Master’s in Mathematics in 2018/2019 with an MSc dissertation in group theory.  

Further education after my Master’s degree was not always the plan. However, after a dialogue with various academics in the Mathematical Sciences Research Centre at Queen’s, a project suggested by Dr Pausinger piqued my interest. I realise now that the choice to continue study was the correct one. I enjoy spending a portion of my day engrossed in a subject that excites me and satisfies my curiosity.

Research interests

• Uniform Distribution Theory

• Group Theory

• Quasi-Monte Carlo Methods