Summer research in School of Mathematics

Project

Graph embedding problems

Project lead

Dr David Hume

Research objective

Graph embedding problems constitute one of the key difficulties in modern machine learning, and a new and useful tool for classifying a wide range of abstract mathematical objects including groups and fractals. This project approaches the problem from a pure mathematics perspective, looking at how we may define a "good embedding" and then quantifying which spaces admit one and when they don't, how badly they fail. Most of these ideas are very new and there are many accessible open problems in the area suitable for undergraduate researchers.

Depending on the interests and background of the student, there are a range of possible objectives including:

(i) construct families of graphs with prescribed embedding properties into a fixed target space

(ii) determine, for a fixed family of graphs, the best target space to embed them into

(iii) explore the relationships between various different measures of a good embedding through new examples

Research pre-requisites

Some understanding of graphs, groups and/or metric spaces would be helpful but not essential.