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Presenting a poster pitch and a poster

Ashleigh Ratcliffe (University of Leicester) - On the Equation x^4-y^4=D

This poster summarises a list of integers expressible as a difference of two rational fourth powers and the known methods used prove which integers are not representable as a difference of two rational fourth powers.

Mingjia Yan (University of Cambridge) - Geometric Field Theory for Elastohydrodynamics of Cosserat Rods

The Cosserat rod provides a mathematical framework for slender bodies that can stretch, shear, twist and bend, in viscous fluids. We demonstrate that the resulting elastohydrodynamic equations of motion, formulated using Cartan's method of moving frames, fits into a geometric field theory where the configuration field takes values in SE(3), the Lie group of rigid motions. This geometric formulation yields coordinate-free equations that are invariant under spatial symmetries. We also build structure-preserving numerical schemes to simulate the rod motions .

Karla Bonic-Babic (University of Oxford) - A Comparison of Three Methods for Estimating the Probability of a Major Outbreak

Early in an infectious disease outbreak, it is often unclear whether transmission will fade out or escalate. We compare three methods for estimating the probability of a major outbreak (PMO) from early incidence data: i) an analytic approach; ii) simulation-based trajectory matching; and iii) a machine-learning classifier trained on simulated outbreaks. All three yield consistent PMO estimates but differ in mechanistic transparency and flexibility. We highlight when each approach is most useful. These tools apply whenever a pathogen invades a new location, not only at the start of an epidemic

Aleksandra Tokaeva (University of Warwick) - Survival strategies in a Stochastic Market Game with Endogenous Prices

We consider a stochastic market model with continuous time and endogenous asset prices, and study how a small agent should behave to survive. We obtain necessary conditions for a small agent’s strategy to be survival, meaning its share of the total market wealth remains bounded away from zero over an infinite time horizon regardless of the strategies used by other agents. This contributes to several previously known results, being the first time when the interaction between big and small agent is considered with focus on construction of survival strategies.

Jane Turner (University of Southampton) - Relative Algebraic K-theory and Exterior Power Operations

Algebraic K-theory is a fascinating field of mathematics with applications in geometry, topology and number theory. My research concerns a certain conjectural presentation of the relative K-groups, verifying that the presentation is valid and constructing additional structure on this presentation.

Inzish Sajid (University of Reading) - A Methodology for Generating Synthetic Quantitative ODE Model Data for Parameter Estimation

Pharmacology and toxicology studies often use compartmental mathematical models to understand how compound concentrations vary throughout the body. Such models require experimental data to inform their parameters. However, such data is costly and not always available, and thus we need to find new ways to parameterise traditional ordinary differential equation models under data-scarce conditions. The poster presents a novel methodology that can be effectively used to parameterise mathematical models when limited data is available.

Sarah-Sonia Balan (University of Manchester) - Emmy Noether: Life and Mathematics

So much of Emmy Noether’s legacy lives on in the language of mathematics, yet behind the concepts that bear her name stood a mathematician who had to fight for the right to exist within the very institutions that needed her most. Invited to Göttingen by Hilbert, she lectured for years without pay or recognition, even as she reshaped algebra and physics. By reading Noether’s mathematics alongside her lived experience, this poster asks a question that still resonates today: whose brilliance is recognised and who continues to feel permitted to imagine themselves at the centre of mathematics.

Caroline Purvis (University of Bath) - Evaporation of a Sessile Droplet into a Confined Atmosphere

The evaporation of sessile droplets is a challenging, industrially relevant problem that has been the subject of intensive multidisciplinary research. Most previous work considers an isolated droplet in an unbounded atmosphere, with relatively little on the effect of confinement of the atmosphere on the evaporation from a droplet and its consequent evolution. We aim to address this using a range of techniques to formulate and solve models for the diffusion-limited evaporation of a droplet in different confined geometries, with our initial work focusing on open- and closed-ended cylinders.

Ayesha Sarwar (University of Glasgow) - Force Balances of Dipolar Dynamos

"The geodynamo, which sustains the Earth’s magnetic field through convectively-driven fluid motion in the outer core, is a fundamental, yet complex process that continues to challenge our understanding. The fluid flow is determined by the balance of forces in the momentum equation. Recent studies have investigated this complexity through scale-dependent and position-dependent analyses, with some focusing on solenoidal forces. We present three-dimensional dynamo simulations in different dynamical regimes to investigate the temporal evolution of forces and their hierarchy.

Ellie Kovachky (University of Hertfordshire) - Searching for Cool Brown T-Dwarf Companions Around Nearby Stars

The investigation of brown dwarves is cruical to understanding vital topics such as star formation, the BD desert, and cosmic evolution. Using cool brown T-Dwarf companions discovered with data from VISTA, DES, and WISE surveys, I inspected 150 candidates to locate binary systems with a nearby star. To complete this, DS9 is used to check the correct optical and infrared filters (Z,Y,J,H) and analyse brightness and movement, whilst GAIA is used to perform proper motion calculations. In conclusion, three different binary systems are found, including a special case of a rather young brown dwarf.

Presenting a poster

Michelle Simons (University of Edinburgh) - Understanding Gell-Mann's Quark Model through SU(3)-described Oscillators

The primary objective of this project involved working out the Lie algebra of the SU(3) group in terms of the algebra of three independent harmonic oscillators, following Schwinger’s oscillator method of angular momentum. Describing the SU(3) Lie algebra in this manner allows for an interpretation of the up, down, and strange quarks in the Gell-Mann quark model as independent harmonic oscillators. This method also explains the v-spin and u-spin analogues of isospin.

Izzy Cole (University of Cambridge) - Modelling Vasculogenesis: the Emergence of a Network to Promote Efficient Transportation

How do networks transport goods efficiently? How do transport networks cope with perturbation and disruption? This is a relevant topic in both biology (where networks emerge to transport nutrients), and engineering (for constructing efficient travel eg. via road and rail networks). In particular, I am studying the developing vascular network in chicken embryos. My project includes 1. analysis of developing network features, 2. topological data analysis – in particular persistent homology, and 3. prediction of network growth via stochastic techniques.

Fan Wu ( Cardiff University) - Measuring Market Risk: A Two-Layer Network Approach

The interconnectedness of the financial market can spread market risk. In this study, we address the market interconnectedness from the perspective of the volatility contagion and the sentiment spillover among the companies. We propose a two-layer network capturing volatility contagion and sentiment spillover on each layer. The properties of this two-layer network are extracted to propose a novel market risk.

Tatiana Kurlina (University College London) - AI in Crystallography: Mathematics exposes Artificial Illusions in material design

Crystallography is the study of solid crystalline materials. AI tried to predict new materials by generating millions of simulated crystals, but failed to recognise thousands of exact & near-duplicates. Comparing crystals reliably requires a geometric approach using equivalence classes, invariants and continuous metrics. Since symmetries break under almost any noise, anyone can generate millions of new-looking crystals through the power of maths rather than AI. Using geometry to rigorously study real objects is growing past mathematical crystallography into a new field, Geometric Data Science.

Reagan Crump (Hendrix College) - Chaos in Piecewise Matrix Transformations.

Based upon a 5-week undergraduate summer research project under the guidance of a professor at Hendrix College, my poster presents an investigation into the dynamics of two-dimensional or three-dimensional iterated maps of the real line, extending work in Linear Algebra courses. I constructed a piecewise linear map from a rotation matrix and a matrix built from eigenvectors, exploring the system and beginning to see evidence of periodic and chaotic behavior.