The IMA National Best Maths Project Competition took place this year on 24 July 2026. This competition recognises the most outstanding undergraduate project work in Mathematics, Statistics, and Operational Research from across UK universities. Ben Le Jeune (Imperial College London) and Alice Henman (University of Durham) were awarded first and second place respectively and will deliver talks based on their respective projects at this celebration event.
Life and Death in Evolution: Topics in Adaptive Dynamics
Alice Henman (University of Durham)
Evolution is a highly complicated and beautiful process which is still yet to and most likely never will be fully understood. Nonetheless, it is a universally familiar concept. What isn’t often considered however, is how we can use mathematics to quantitatively model the process, as is the purpose of this paper.
In this thesis we will be using the tool of adaptive dynamics to study the different outcomes of evolution for various different population models. This involves extending dynamical systems to encode evolutionary behaviour by mutating a chosen parameter in the model and investigating how it affects the success of the population. We will begin by introducing the key tools and definitions of adaptive dynamics alongside a basic example using the logistic growth model. The second chapter introduces the concept of evolutionary suicide and finds that evolution can draw a population to extinction if trait evolution pushes the system across a catastrophic bifurcation. The third chapter looks into evolutionary branching, exploring the conditions for it to come about. Notably, an evolutionary stationary point must be able to support the coexistence of two resident trait values within the population, and these branches must evolve apart from one another to produce dimorphism.
Finally, branching and extinction are combined to form a cyclic evolutionary trajectory to reflect the red queen hypothesis in the fourth chapter. In order for this to occur the trajectory of the resident trait pair formed after branching must be able to escape the coexistence region before it can be pulled towards a convergent evolutionarily singular strategy.
Stochastic resetting for general inter-particle structures
Ben Le Jeune (Imperial College London)
In this work, we analyse the steady-state statistics of diffusive particles undergoing stochastic resetting. While much of the literature assumes a fixed reset distribution, we allow particles to instead reset to the positions of other particles. We begin with the simple and known case of a “chain” of particles resetting to one another, computing the single-particle moments and twoparticle correlators. We then extend the tools to other graphs, and investigate extensions to the chain case, such as variable resetting rates. We then conclude with a general theory for resetting systems defined on arbitrary weighted graphs, showing that a static-distribution “anchor” is needed to prevent delocalisation.