The theory of random matrices was introduced by John Wishart (1898–1956) in 1928. The theory was then developed within the field of nuclear physics from 1955 by Eugene Paul Wigner (1902–1995) and later by Freeman John Dyson, who were both concerned with the statistical description of heavy atoms and their electromagnetic properties. In this snap- shot, we show how mathematical properties can have unexpected links to physical phenomenena. In particular, we show that the eigenvalues of some particular random matrices can mimic the electrostatic repul- sion of the particles in a gas.

It has always been the dream of mankind to predict the future. If the future is governed by laws of physics, like in the case of the weather, one can try to make a model, solve the associated equations, and thus predict the future. However, to make accurate predictions can require extremely large amounts of computation. If we need seven days to compute a prediction for the weather tomorrow and the day after tomorrow, the prediction arrives too late and is thus not a prediction any more.

We describe a connection between quantum mechanics and nonlinear wave equations and highlight a few problems at the forefront of modern research in the intersection of these areas.

We explore mathematical models for physical problems in which it is necessary to simultaneously consider equations in different dimensions; these are called mixed-dimensional models. We first give several examples, and then an overview of recent progress made towards finding a general method of solution of such problems.

Graphs are mathematical objects composed of a collection of “dots” called vertices, some of which are joined by lines called edges. Graphs are ideal for visually representing relations between things, and mathematical properties of graphs can provide an insight into real-life phenomena. One interesting property is how connected a graph is, in the sense of how easy it is to move between the vertices along the edges. The topic dealt with here is the construction of particularly well-connected graphs, and whether or not such graphs can happily exist in worlds similar to ours.