The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing in September 2021.
This project will be supervised by Dr. Robert Johnson and Dr. Felix Fischer.
Voronoi games are models of agents competing for a share of a domain under the assumption that each of them attracts points which are closer to them than to a competitor. For example, suppose that political opinions are represented by points in a real interval (thought of as a left/right spectrum) and individuals support the party whose position is closest to their own. If there are two parties positioning themselves to compete for vote share, the equilibrium position is for them both to occupy the centre ground (the position of the median voter). This is the well-known Median Voter Theorem.
Voronoi games (also known as facility location problems) are a classic part of operational research with a body of work on them. However most of this is in the context of continuous domains such as the real interval example above. This project will study analogues in discrete settings (agents operating on a graph) where much less is known and there are many interesting questions.
A particularly intriguing example is the discrete hypercube (the graph whose vertices are all 0-1 strings of length d with two vertices adjacent if they differ in exactly one position). The discrete hypercube is much studied and important combinatorial object so this is a mathematically natural setting. It can also be viewed as a discrete variant of the voting example above in which opinions are represented by a stance on each of d binary issues rather than a point on continuous spectrum.
Some background in combinatorics and graph theory would be highly desirable.
The application procedure is described on the School website. For further inquiries please contact [Email Address Removed] and [Email Address Removed]. This project is eligible for full funding, including support for 3.5 years’ study, additional funds for conference and research visits and funding for relevant IT needs. Applicants interested in the full funding will have to participate in a highly competitive selection process.