# Members' Papers

## Various Speakers

This annual event gives our members the chance to shine by presenting their own papers. The usual time is divided into a number of short lectures by members of the Invariants society. All members are welcome to give a paper!

### Catrin Campbell-Moore, “Skolem’s paradox”

Skolem’s paradox shows a contradiction between two theorems of mathematics: Lowenheim-Skolem’s theorem, showing that there is a countable model for first-order set theory, and the existence of uncountable sets. Is this a paradox? If so, then we should reject set theory. We will outline the paradox and show how it can be avoided. Although not an outright contradiction, the ‘paradox’ is still worrying since it shows that set theory cannot pin down our intuitive notion of “countable” and that set theory can ‘misinterpret’ its axioms.

### Kris Joanidis, “The (meta)mathematics of reproduction”

Ever wondered what distinguishes living things from robots? Could the essential difference be that robots are incapable of reproduction? This question was answered by Stephen Cole Kleene in 1938. This talk will provide a gentle introduction to his famous theorem and explore a couple of interesting consequences.

### Thomas Woolley, “Diffusion of the Dead”

Knowing how long we have before we interact with a zombie could mean the difference between life, death and zombification. Following the recent success of mathematical tools being used to understand zombies, we extend these previous models to encapsulate the zombie population shuffling randomly over space. This mathematical formulation allows us to derive exact and approximate interaction times, leading to conclusions on how best to delay the inevitable meeting. Interaction kinetics are added to the system and we consider under what conditions the system displays an infection wave. Using these conditions, we then develop strategies which allow the human race to survive their impending doom.