Meet Simon Goodwin, Statistics summer scholar

Every summer, the Department of Statistics offers scholarships to high-achieving students so they can work with staff on real-world projects. Simon Goodwin, below, is working with Dr Jesse Goodman on random graph dynamics and hitting times.

Simon’s summer scholarship is related to the study of random graphs, looking at how to investigate networks that look as if they are random or pseudo-random, like social networks, family trees or the global flight network.  His task in particular is looking at the nodes in these structures that are hard to reach by moving randomly, and what this means for the structure of the graph as a whole.

You can conceptualise it like this: Produce a random graph by connecting pairs of vertices uniformly at random. Then run a random walk on this random graph: at each step, move to a uniformly chosen neighbour of the current position. The hitting time is the number of steps needed to reach a particular target vertex, and it varies in a particular way depending on the size of the random graph.

Simon’s work looks at the effect of changing the random graph. Between each random walk step, he might “rewire” some edges: pick a fraction of edges, disconnect the vertices on either side, then randomly reconnect those vertices to see if these graph dynamics make it faster (or slower) to reach the target vertex.

“Looking at the structure of these random theoretical objects we can learn about vast real-world networks that have no clearly apparent structure,” Simon explains. “The results I am trying to find would also have theoretical applications in the study of random graphs.”

Simon is about to start his third year studying maths and statistics: “My main interest is in pure maths, but I am also very interested in theoretical statistics, mainly in probability. I am intrigued by all things random.”

In fact, he dropped physics for statistics last year, “and I haven’t regretted it for one moment – sorry physics! I am mainly interested in probability but I have also enjoyed learning about data analysis and I have an interest in statistical computing.”

He adds, “Probability is such an interesting field, as it has a strong theoretical backing while also having many obvious applications such as games with dice and cards, as well as many less obvious applications, from financial-market analysis to quantum physics.”

Simon is hoping to become an academic: “I hope to continue into postgraduate study and then spend the rest of my life studying and teaching what I love.” When he’s not studying, Simon loves playing video games and roleplaying games like Dungeons and Dragons, as well as walking around the scenic spots of Auckland.

• For general information  on University of Auckland summer scholarships, click here.