Abstracts
Angus Matthews — The F-Conviviality graph
In this talk we will introduce the F-conviviality graph, a concept from matroid theory, and discuss its connections to model theory.
Anna Sigalou — Long-term behaviour social decision-making rules
Faced with choices under uncertainty, social animals source information from their conspecifics. This social information can help mitigate against poor personal information, and ameliorate decision-making quality; but it may also amplify poor information, leading to poor information cascades. A crucial factor in determining the outcome of social decision-making is the way social information is used by animals -i.e. their decision-making strategy. By modeling decision-making as a Markov process, we can get insights about the long-term tendencies of different decision-making strategies. Subsequently we can infer which strategies are more prone to traits such as poor information cascades. Lastly, by comparing the observed behaviour of different species and the predictions on the aforementioned models, we can make educated guesses about the underlying decision-making mechanisms these species follow.
Ben De Smet — Manifolds in O-minimal Structures
Reasons to come to this talk are manifold.
Benjamin Morris — A Diagram Category for Non-Orientable Surfaces
In this talk I will present the construction of a discrete two-parameter tensor category that generalises the Temperley-Lieb category, and has a diagrammatic calculus consisting of embedded curves in a once-bounded surface.
Benjamin Morris
Poster
Calliope Ryan-Smith — Domination and boundedness
Bounding and domination are relationships between sequences of numbers that are studied in set theory and give us insight into the structure of the set of real numbers. I shall present an overview of these relations and describe their importance to set theory.
Gautam Chaudhuri
Poster
Hope Duncan — The Axiom of Choice
Studying the Axiom of Choice gives many fascinating insights into what we deem to be intuitive or unintuitive across many fields of mathematics. We can also consider the very foundations of mathematics, what should we assume to be true and why? In this talk, I will introduce the axiom of choice and its equivalences, give some consequences of both assuming and not assuming choice, and finally give the longest standing open question in set theory.
Lenny Greenfield — Orbits on Graph Colourings
We consider the set of all possible colourings of a finite graph using a finite number of colours. We define an action of the automorphism group of the graph on the set of all colourings where two colourings are equivalent if there exists an automorphism that moves the colours of vertices in one colouring to the colours of vertices in the other colouring. In this talk we will discuss methods for calculating the number of distinct colourings when the automorphism group action on the graph is primitive.
Luca Seemungal — Doing my Nash-ional Service
Whereas John Forbes Nash Jr. is most well-known on the one hand amongst the general public for being the subject of the 2001 film 'A Beautiful Mind' and on the other hand amongst the scientifically-minded masses for the Nash equilibrium in game theory, for those of us who forever dwell in the house of geometric analysis he is celebrated for his remarkable Embedding Theorem (Annals of Mathematics, 1956), which completely and perfectly answers fundamental questions raised by the extrinsic-intrinsic counterpoint of the 18th Century theory of differentiable surfaces on the one hand and the late 19th Century theory of Riemann surfaces on the other; in doing so, Nash initiates geometric analysis and the modern theory of PDE. In this talk I humbly do my duty as a geometric analyst and narrate this story, wherewith I hope to impart on you some sense of just how momentous this theorem is, which to my mind is one of the most dazzling theorems of the previous century. (Credit for title: Calli.)
Matthew Asker — Spatial Structure and Environmental Dynamics in Microbial Populations
Microbial populations evolve within spatially structured and dynamically changing environments, a reality often overlooked by classical modelling approaches. From microbial infections spreading across host organs to environmental pollutants altering ecological niches, understanding the effects of and interplay between spatial structure and environmental change is essential for developing insights into the evolutionary dynamics of microbial communities. Here, we present a comprehensive analysis of a two-species metapopulation model, incorporating selection bias, to investigate how microbial species evolve while competing for a varying level of resources. Our analytical framework provides insights into the non-trivial behaviour of the fixation probability and mean fixation time across network structures in one dimension. Additionally, Monte Carlo simulations offer a deeper understanding of the complex dynamics on a two-dimensional lattice, extending beyond the scope of analytical predictions. By combining analytical and computational methodologies, we uncover the rich dynamics underlying microbial population evolution in spatially structured and dynamically changing environments.
Matthew Vine — Parametric Instabilities of Alfvén-Gravity Waves
In Boussinesq fluids, instabilities of small-amplitude internal gravity waves (IGWs) can be attributed to resonant triad interactions between three IGWs. The picture is a little more complex when we introduce a uniform background magnetic field. Under this configuration, two types of wave can partake in the resonant interactions: pure Alfvén waves and hybrid Alfvén-gravity waves. We contour the growth rate of such instabilities numerically using a Floquet solver and identify which types of wave are interacting to produce the instabilities shown. This work is relevant in stably-stratified fluids permeated by magnetic fields, with radiative zones in stellar interiors being a notable example.
Max Hughes — A Postgrad's Guide to Outreach
TBD
Mervyn Tong — Graph-theoretic tameness via model theory
Tameness is a desirable attribute in every area of mathematics. I present two problems in graph theory that reflect two facets of combinatorialists' pursuit of tameness in graphs: Zarankiewicz's problem, which asks for bounds on the size of a graph that omits a certain configuration, and Szemerédi's regularity lemma, which allows a graph to be partitioned into well-behaved cells. Along the way, I discuss how model theory helps us to both understand the reason behind such tameness phenomena and provide better bounds.
Norah Almasoud
Poster
Puchong Paophan
Poster
Richard Mann — Collective decision-making by rational agents
The decisions made by others are a valuable source of information about the world, because they may have knowledge that we lack. This means that when one agent makes a given choice, it can induce others to do so as well. In this talk I will describe a theory of rational agents who optimally utilise the social information provided by others, and explore the dynamics this produces at the individual and group level. In particular, I will show how the implicit beliefs such agents hold about the physical and social environment shape their response to each other, and how changes to the environment that conflict with these beliefs can dramatically alter collective behaviour and impact the success of groups.
Sarah Almateari
Poster
Thomas Bernert
Poster
Xiangyu Wu
Poster
Yang Lu — Building a Numerical Wave Tank
In this talk, I will present a computational tool for simulating 3D nonlinear water waves arising in the context of high-amplitude waves generated by in-house experimental wave basins in the maritime industry. The analysis is based on a fully nonlinear potential-flow water-wave model, and the numerics are conducted through a consistent space-time variational discretisation implemented in Firedrake. Three stages of the developing process, namely mathematical, numerical and computational modelling, are covered for the so-called 'numerical wave tank'.
Yijun Fu
Poster