TUESDAY, 26 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 1206c
12:10-12:30	UG1154 Lejie Xu Integral geometry Individual Project Integral geometry is closely related to convex geometry and valuation theory. This talk gives a brief introduction to the field of classical integral geometry on convex sets in the Euclidean space. We look at the landmark of this area - Hadwiger's characterization theorem. We also discuss the intrinsic volumes, which help characterize all continuous rigid motion invariant valuations defined on the lattice of polyconvex sets. We end by some integral geometric formulas and concrete examples. Observers: Arend Bayer and David Quinn
12:40-13:15	UG1147 Victor Gaino Topos Theory Dissertation Observers: Arend Bayer and David Quinn
13:25-14:00	UG1387 Jake Walsh Geometry of Complex Manifolds Dissertation Observers: Arend Bayer and David Quinn

TUESDAY, 26 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 3211
12:10-12:35	UG1115 Boren Gu, Blane Heerey-Piszkoski, Gavin McWhinnie, Mak Pehar Quivers and Gabriel's theorem Group Project In this talk, we introduce the algebraic study of quivers (essentially finite directed graphs) via means of their representations. In doing so, we stumble upon the first major classification theory for representations of quivers - Gabriel's theorem, which we proceed to outline and give motivation for, while building up all of the requisite machinery. Throughout this we unveil unusual connections with other areas of mathematics, such as the study of Lie algebras, category theory, and more. Observers: James Lucietti and Ana Rita Pires
12:45-13:10	UG1144 Leilani Fam, Benjamin Gorrie, Sophie Kerfoot, Lucy McPhail, Hannah Coote Paradoxes in Mathematics Group Project Observers: James Lucietti and Ana Rita Pires
13:20-13:55	UG1145 Luke Appleby The Derived Category Dissertation Observers: James Lucietti and Ana Rita Pires
14:10-14:35	UG1146 Jessica Bossom, Ronan Garrett, Luke Mitchell, Arjun Nanning Ramamurthy, Samuel Hummel Locales and Intuitionistic Logic Group Project Intuitionistic logic is classical logic without the law of excluded middle. We will show how this logic can be modelled algebraically as a structure called a Heyting algebra. We will see that restricting to a special subclass of these algebras, we can uncover a fascinating topological interpretation. Observers: Nick Sheridan and Joan Simon
14:45-15:20	UG1275 Emily Georgiadou Patchworking curves Dissertation Observers: Nick Sheridan and Joan Simon
15:30-16:05	UG1278 Diana Bergerova Hilbert schemes and coloured partitions Dissertation Observers: Nick Sheridan and Joan Simon
16:15-16:50	UG1389 Lucy Spouncer A Theory of Higher Operads Dissertation Observers: Tudor Dimofte and Pavel Safronov
17:00-17:20	UG1391 Rafael Krajewski-Siuda Condensed/pyknotic geometry Individual Project Observers: Tudor Dimofte and Pavel Safronov
17:30-17:55	UG1156 Sadie Bell, Jac Fearnley, Nikita Jegorovs, Jesse Wilson Measures of biodiversity Group Project Observers: Tudor Dimofte and Pavel Safronov

TUESDAY, 26 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 4325b
12:10-12:30	UG1119 Adam Warren Exploring Black Holes, an Introduction to General Relativity Individual Project Observers: Jacques Vanneste and Max Ruffert
12:40-13:05	UG1171 Jocelyn Tung, Zixuan Zhang Draw me a star Group Project Observers: Jacques Vanneste and Max Ruffert
13:15-13:50	UG1167 Meg Wilkinson Bohemian Rhapsody Dissertation Bohemian Matrix families are matrices with entries drawn from a finite, discrete set. Traditionally these sets were integers but now encompass a diverse array of populations within the real and complex numbers. The eigenvalues of families of Bohemian Matrices produce beautiful, complex images that are significantly different depending on the structure of the matrix. In this talk, we delve into the properties of eigenvalues within distinct structured families of Bohemian Matrices, including complex symmetric, Toeplitz, and circulant matrices. Density plots of these eigenvalues can exhibit profound connections to fractals, and we discuss the Sierpinski-gasket-like structures found in Unit Toeplitz Upper Hessenberg matrices with the cube roots of unity as the population of interest. Furthermore, we explore the intimate relationship between Bohemian Matrices and polynomials through companion matrices. Despite these insights, numerous unanswered questions persist regarding these underlying structures of Bohemian Matrices, which we identify throughout the talk. Observers: Jacques Vanneste and Max Ruffert
14:00-14:35	UG1177 Xinger Tang Numerical Discretization and Preconditioning for Optimization Problems with PDE Constraints Double Project Observers: Ben Leimkuhler and Tom Mackay
14:45-15:20	UG1192 Mark Kennedy The geometry of thermodynamics Dissertation Observers: Ben Leimkuhler and Tom Mackay
15:30-15:55	UG1193 Owen Cray, Esther Shu Sian Ng, Alexandra Rivers, Yuting Zhang, Thenura Ariyananda A conceptual model of climate uncertainty Group Project Observers: Ben Leimkuhler and Tom Mackay

TUESDAY, 26 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 6201
12:10-12:30	UG1307 Noah Wells Tests of General Relativity Individual Project Observers: Guopeng Li and Hiro Oh
12:40-13:15	UG1245 Cassia Edwards Families of circles Dissertation Observers: Guopeng Li and Hiro Oh
13:25-14:00	UG1250 Elliot Ede Methods from Analysis in Topology Dissertation Observers: Guopeng Li and Hiro Oh
14:10-14:35	UG1212 Xiangkun Kong, William Styles, Siddharth Berera Baire 1 functions and derivatives Group Project Observers: Martin Dindos and Linhan Li
14:45-15:20	UG1251 Robbie Allerhand Real Variables and Fourier Analysis Dissertation Observers: Martin Dindos and Linhan Li
15:30-15:55	UG1362 Ritam Dey, Eloise Wilson Conformal diagrams in general relativity Group Project Observers: Martin Dindos and Linhan Li
16:10-16:35	UG1225 Jilin Chen, Yifan Du, Yuning Zhang, Winfred Zhou, Guidian Chen Large deviation principles and its applications Group Project Observers: Tony Carbery and Jonathan Hickman
16:45-17:20	UG1265 Boyun Jiang Various approaches to the Dirichlet problem Dissertation Observers: Tony Carbery and Jonathan Hickman

TUESDAY, 26 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 6301
14:10-14:30	UG1199 Yuxuan Yan Electromagnetic theory of complex materials Individual Project This presentation summarizes some important topics in the electromagnetic theory in complex materials. It focuses on the formulation of Maxwell's equation, the eigenanalysis of plane waves, the dyadic Green function method for solving the electromagnetic fields and three homogenization formalisms. Observers: Des Higham and Adri Olde Daalhuis
14:45-15:10	UG1207 Xiaoyu Chen, Imogen Sole, Mac Walker, Xian Wang, Elizabeth Wilson Gaussian processes for machine learning Group Project Observers: Des Higham and Adri Olde Daalhuis
15:20-15:45	UG1208 Timofei Averkiev, Alexey Dronov, Ed Grosvenor, Yuxin Li, Pranith Praveen Image analysis Group Project Observers: Des Higham and Adri Olde Daalhuis
16:00-16:25	UG1160 Xilin Hou, Enya Liu, Joanna Tulloch, Tom Yuan Elliptic functions Group Project Observers: Des Higham and Adri Olde Daalhuis
16:35-17:10	UG1139 Yuanhao Jiang Score-Based Diffusion Techniques and Diffusion Map method for Generative Modelling Dissertation This talk presents an exploration to generative modelling, with a primary focus on score-based generative modelling using stochastic differential equations (SDEs). The score-based diffusion techniques utilise the diffusion processes to model and generate complex data distributions accurately. By examining the theoretical underpinnings and practical applications of score-based models, we aims to improve the versatility of SDEs in capturing the essence of high-dimensional data spaces by introducing the configuration-dependent SDEs. We also extends an introductory yet insightful foray into generative modelling using diffusion maps, with a conceptual connection to the score-based method. It broadens the perspective on generative modelling by considering its potential intersections with manifold learning techniques. Observers: Des Higham and Adri Olde Daalhuis
17:20-17:55	UG1164 Qianqi Jia, Siyuan Chang Estimating Dimension Double Group Project In our presentation, we will introduce the fundamental concepts of fractals and the Chaos game, followed by an exploration of fractal dimension and methods for estimating dimensions, specifically focusing on the Box-counting and the Two-Nearest Neighbour (Two-NN) methods. Our primary emphasis will be on the Two-NN method, discussing its significance and advantages in determining high-dimensional data. Then we will present our experimental results from applying the Two-NN method to estimate the dimensions of the Sierpinski triangle and carpet, the MNIST dataset that is commonly used in machine learning, and a set of images we have chosen. Observers: Des Higham and Adri Olde Daalhuis

TUESDAY, 26 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 1501
16:10-16:30	UG1269 Bence Szilagyi Moment problem Individual Project Observers: Nikolaos Bournaveas and Leonardo Tolomeo
16:40-17:15	UG1194 Mary O'Brien Complex dynamics Dissertation Observers: Nikolaos Bournaveas and Leonardo Tolomeo
17:25-18:00	UG1283 Ziqian Fang Solitary waves for the the nonlinear Schrodinger equation Dissertation Observers: Nikolaos Bournaveas and Leonardo Tolomeo

TUESDAY, 26 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 5327
16:10-16:35	UG1201 Jack Biss, Thomas Carswell, Will Shennan, Ronan Blackwood The doubtful job security of professional sports trainers Group Project Observers: Nicole Augustin and Natalia Bochkina
16:45-17:10	UG1135 Yicheng Li, Zeyu Yang Nonparametric Bayesian Methods Group Project Observers: Nicole Augustin and Natalia Bochkina
17:20-17:55	UG1322 Abdulrahman Badmus State space models, particle filtering, and graphs Double Project Observers: Nicole Augustin and Natalia Bochkina

WEDNESDAY, 27 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 1501
11:10-11:35	UG1242 Regan Hwang, Jun Xian Loh, Anastasia McMillan Set-Theoretic Solutions to the Yang-Baxter Equation Group Project Our talk will focus on the Yang-Baxter equation, a fundamental mathematical equation with broad applications in various disciplines. The Yang-Baxter equation arises in the study of algebraic structures, topology, and quantum mechanics, making it a topic of significant interest. The objective of our work is to explore different aspects related to the Yang-Baxter equation, with a particular emphasis on its solutions and their connections to algebraic structures such as rings, braces, semi-braces, and quasigroups. Observers: Jose Figueroa-O'Farrill and David Quinn
11:45-12:20	UG1292 Nikolai Perry Knot invariants and quantum groups Dissertation Observers: Jose Figueroa-O'Farrill and David Quinn
12:30-13:05	UG1133 Guillem Ribas Pescador Topics in quantum information Double Project Observers: Ana Rita Pires and Chris Smyth
13:15-13:50	UG1386 Taraneh Latifi Seresht Unique factorisation in quadratic fields Dissertation Observers: Ana Rita Pires and Chris Smyth

WEDNESDAY, 27 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 5205
11:10-11:35	UG1226 John Clifford, Jin Li, Siya Li, Paula Sparrow On the effectiveness of writing activities in a first year mathematics undergraduate course Group Project Observers: Paola Iannone and Simon Taylor
11:45-12:20	UG1188 Elinor Flavell The Organica of Van Schooten Dissertation The 17th century Dutch mathematician, Frans van Schooten, is probably best known for his translation of Descartes's "La Geometrie" from French into Latin, thereby introducing it to the wider scientific community. However, this talk will focus on an original work of Van Schooten, his "Organica", by providing an original translation from Latin into English. The majority of the Organica is an introduction to the different mathematical methods and physical apparatus we can use to construct conic sections and includes an appendix on solutions to cubic equations. This talk will begin by looking at one of Van Schooten's methods for drawing an ellipse. We will then focus on the appendix detailing Van Schooten's approach to solving cubic equations; how it differs from other mathematicians at the time and the connection to conic sections. Throughout, we will look at the geographical, historical and mathematical context in which Van Schooten worked. Of particular interest is a shift in the perception of geometry among scientists at the time. Observers: Paola Iannone and Simon Taylor
12:30-12:55	UG1176 Yuxin Bi, Ariff Mohd Rahdi, Natalie Reilly, Yemin Tang Benchmarking Techniques Group Project Observers: Paola Iannone and Simon Taylor
13:10-13:35	UG1217 Yichao Wang, Haoyuan Zhang, Xiyan Zhou Investigations into data visualisation for making robust interpretations under uncertainty. Group Project Observers: Charlotte Desvages and Robert Bickerton
13:45-14:20	UG1356 Siying Chen The impact of six different regions of Africa on the contemporary American gene pool Dissertation Observers: Charlotte Desvages and Robert Bickerton
14:30-15:05	UG1305 Yuzhou Chen Stochastic Resonance in Climate Models Double Project Observers: Charlotte Desvages and Robert Bickerton
15:15-15:50	UG1152 Ruben Mitchell, Qi Qiu, Wanxue Xu The Travelling Salesperson Problem Double Group Project Observers: Leyli Mammadova and Steven O'Hagan
16:00-16:35	UG1353 Freya Whittaker Divine patterns: geometry in Islamic art Dissertation Observers: Leyli Mammadova and Steven O'Hagan
16:45-17:20	UG1311 Mayez Haris Incorporating uncertainty into model diagnostic plots Dissertation Model diagnostic (MD) plots are a visual tool used to evaluate the quality of the fit of a linear regression model. Due to their visual nature, their interpretation is highly subjective. This talk aims to explore the uncertainty and variability present in the interpretation of MD plots, and how it could be made more consistently correct among undergraduate mathematics students. First, the talk will discuss the use of the lineup protocol, a procedure which formalises the incorporation of the hypothesis testing framework into visual inference. The talk will discuss its motivation and potential uses, along with examples for the audience to participate in. Additionally, a survey using the lineup protocol was conducted using to gain insight into how mathematics students at the University of Edinburgh who had previously completed introductory statistics courses viewed and interpreted MD plots. The results from this survey guided the development of a web application using the Shiny package in R, which will be explained and demonstrated in the talk. The application allows students to explore how MD plots may vary under repeated sampling and the importance of accounting for sampling errors in statistical analysis. The application's expected use is in the university's Statistics (Year 2) course, where undergraduate mathematics students are introduced to MD plots for the first time. Observers: Leyli Mammadova and Steven O'Hagan

WEDNESDAY, 27 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 6206
11:10-11:35	UG1241 Alexis Charalambous, Elyse Jordan Paul-Van Leeuwen, Lily Seeley Mathematics and programming: how much is programming embedded in the teaching of mathematics at university level? Group Project This presentation delves into the current state of programming integration within UK mathematics degrees, exploring both the extent of its incorporation and student perspectives on its implementation. We collected data from university websites and course catalogues to analyse computer programming requirements, utilised languages, assessment methods at 27 UK universities. Additionally, we survey 52 mathematics students from the University of Edinburgh to understand student perceptions of programming within their degree. Our findings reveal almost all universities require computer programming as part of their mathematics curriculum. R was found to be the most used language in mathematics degrees, used almost exclusively in statistics courses. However, universities typically offer more computer programming in non-statistics courses, suggesting a larger variation among languages in these courses. Interestingly, closed-book examinations for programming modules have risen since 2017, diverging from expectations based on the mathematics benchmark statement. Additionally, while some correlation exists between university ranking and the number of offered programming courses, it likely reflects the broader course offerings of Russel Group universities rather than a stronger emphasis on programming itself. From the student survey, we identify a link between familiarity with programming and enjoyment, potentially linked to both increasing mathematical ability and the dedication required for mastering programming. Although students acknowledge the relevance of programming to their studies, their certainty regarding its contribution to their mathematical understanding remains lower. Observers: Skarleth Carrales and Richard Gratwick
11:45-12:10	UG1227 Pablo Ortuño Floría, Andrew Shaw, Chenrui Xu, Alexander Bell An Introduction to Proof in UK universities Group Project The major emphasis placed on proof is one of the greatest difficulties university mathematics students experience at the beginning of their degrees. Many universities in the UK run an "introduction to proof" course, where the differences in the content used create a wide variety of attitudes that students have towards proof. In this talk, we categorise these courses in Russell Group universities by analysing their syllabi, and investigate how the content to which students are exposed to during their introduction to proof affects their attitude and perception of it. Observers: Skarleth Carrales and Richard Gratwick
12:20-12:55	UG1214 Andi Dicu An invitation to C*-algebras Double Project Observers: Skarleth Carrales and Richard Gratwick
13:05-13:30	UG1262 Adil Ali, Kaden Blakey, Feifan He, Stewart Ross How well can AI do in mathematics assessments? Group Project Observers: Richard Gratwick and Kit Searle
13:40-14:05	UG1289 Benjamin Chooyin, Jack Fortune, Rachel Hollingsworth, Heather Napthine, Mitchell McLachlan Automation of SQA Advance Higher STEM examinations Group Project The integration of automated assessments is becoming standard practice for Science, Technology, Engineering and Mathematics (STEM) disciplines at the university level. Accelerated by the COVID-19 pandemic, the shift towards online assessments for examinations has highlighted numerous advantages, including increased efficiency, reduced grading bias, and improved feedback for students. This presentation explores the feasibility of utilising the System for Teaching Assessment using a Computer Algebra Kernel (STACK) for automating Scottish Qualification Authority (SQA) Advanced Higher Mathematics and Physics examinations. Upon converting an examination paper from each subject into STACK's online format, it was discovered that whilst most questions were suitable for automation, some required adjustments. Subsequent analysis showed that their core objectives could still be assessed using STACK. This prompted a review of existing educational frameworks and SQA's core assessment standards, leading to the development of a custom taxonomy aligned with the aims of the Advanced Higher Mathematics and Physics courses. This tailored taxonomy justified necessary modifications allowing for the automation of additional marks whilst preserving the integrity of the original assessment objectives. This presentation provides an overview of the process involved in translating the existing assessments of these courses into STACK. In application, this procedure resulted in the successful translation of 81% of the marks from the SQA's 2019 Advanced Higher Mathematics paper and 69% of the marks from the SQA's 2019 Advanced Higher Physics paper into an automated format. Observers: Richard Gratwick and Kit Searle
14:15-14:50	UG1314 Henry Le Cornu Finite difference schemes and sound synthesis Double Project Observers: Kit Searle and Wei En Tan
15:00-15:25	UG1239 Amina Abid, Oliver Gobie, Lucy Magenis Classroom practices in undergraduate mathematics Group Project Observers: Kit Searle and Wei En Tan
15:35-16:00	UG1240 Maria Christodoulidou Manitara, Ana Rivera Montero, Prapti Maitra Assessment practices in university mathematics Group Project Observers: Kit Searle and Wei En Tan

WEDNESDAY, 27 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 4325c
12:10-12:35	UG1117 Zongsheng Liu, Yu Zhang Mathematical Optimization Models and Algorithms for Hospital Emergency Departments Facility Layout Group Project This report delves into the optimization of multi-floor facility layouts, with a special focus on hospital emergency departments. By developing and validating mathematical models with real-world hospital data, we aim to enhance service quality and operational efficiency through optimized multi-floor layouts. We introduce the Mixed Integer Second-Order Conic Optimization (MISOCO) formulation for the Multi-Floor Layout Problem (MFLP), showcasing its flexibility in handling real-life scenarios through comprehensive trade-off evaluations and the integration of evacuation protocols. Further, the report expands on the Multi-Floor and Multi-Row Layout Problem, proposing a two-stage approach that incorporates vertical space planning, thus improving layout design efficiency by strategically utilizing the white space among departments. Through computational experiments, solution visualizations, and discussions on key aspects such as the totally unimodular property, trade-offs, and potential constraints, we offer valuable insights into the efficacy and practical application of our models. This contribution is significant to the advancement of multi-floor and multi-row facility layout optimization, particularly within hospital emergency departments, laying the groundwork for further scholarly inquiry and practical enhancements in multi-floor facility functionality and efficiency across various sectors. Observers: Tim Cannings and Daniel Paulin
12:45-13:20	UG1138 Pablo Denis Gonzalez de Vega, Simeon Horner, Huaying Wang Statistical methods for the analysis of literature and social media texts Double Group Project Observers: Tim Cannings and Daniel Paulin
13:30-14:05	UG1182 Muyang Liu How good is this medical device? Bayesian mixed models for agreement measures Dissertation Observers: Tim Cannings and Daniel Paulin
14:15-14:50	UG1238 Thomas Lai Using empirical likelihood for statistical analysis Dissertation Observers: Tim Cannings and Daniel Paulin
15:00-15:20	UG1249 Alexander Buck Modelling the Traffic In Cloud Systems Individual Project Observers: Jörg Kalcsics and Andreas Grothey
15:30-16:05	UG1255 Bence Kaszas Comparison of different methods for variable selection in the context of generalised additive models Dissertation Observers: Jörg Kalcsics and Andreas Grothey
16:15-16:40	UG1267 Zoe Armstrong, Ye Liu, Louis MacDonald, Maximilian Walden Time-Series Models for Predictive Forecasting of Wind Energy Group Project As the world transitions into a future more reliant on renewable energy such as wind, fears surrounding the reliability of wind power unveils the necessity to predict behavior in wind energy capacity to reduce uncertainty. In this project, we investigate multiple models and compare to popular benchmarks. We first test temporal methods, specifically the popular benchmark of ARIMA and a temporal XGBoost model, to predict the simulated wind metric 48 hours into the future, with model performance being very similar. Afterwards, we investigate the inclusion of a spatial element in prediction to both generalise and widen applicability of models. Prediction across space was investigated in the benchmark of Ordinary Kriging and spatial R-INLA, and compare model results finding that R-INLA has substantial improvements over the benchmark. We investigate spatio-temporal versions of the best versions of our experimental models in the form of spatio-temporal XGBoost and separable spatio-temporal R-INLA. While separable spatio-temporal R-INLA was found to have better accuracy and high generalizability, spatio-temporal XGBoost spends less time for similar results. Comparing the use cases of the models, we find that spatio-temporal XGBoost is more applicable in scenarios where real-time predictions or rapid model training are crucial, thanks to its faster training times. On the other hand, R-INLA is more suitable for situations where precision and interpretability are paramount, even if it requires longer training times. For further extensions, we recommend testing on real life data in various locations and time periods to further validate findings, as well as testing of more methods, such as neural networks. Observers: Jörg Kalcsics and Andreas Grothey
16:50-17:15	UG1316 Matthew Forsyth, Oscar Youngman Group Project on Algebraic Geometry Group Project Observers: Vanya Cheltsov and Pavel Safronov
17:25-18:00	UG1370 Edward Isayev Geometry of Fano varieties Dissertation Observers: Vanya Cheltsov and Pavel Safronov

WEDNESDAY, 27 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 1206c
13:10-13:35	UG1189 Nana Cheng, Anna Dougan, Amy Galley, Queena Wang Comparison of Methods for Estimating Excess Deaths in the UK During the Covid-19 Pandemic Group Project Observers: Vanda Inacio De Carvalho and Andreas Grothey
13:45-14:10	UG1118 Yujie Chu, Pia Fullaondo, Qinqing Li, Jacko Zhou Data Visualization: Theory and Practice Group Project Observers: Vanda Inacio De Carvalho and Andreas Grothey
14:20-14:45	UG1327 Ruxuan Lai, Beth Robinson Optimization methods for allocating students to projects Group Project Observers: Stefan Engelhardt and Jacek Gondzio
14:55-15:20	UG1237 Wenyue Cao, Xinwen Xu Statistical modelling of directional data Group Project Observers: Stefan Engelhardt and Jacek Gondzio
15:30-16:05	UG1170 Niharika Reddy Peddinenikalva Mathematical Optimization for Scheduling Problems Dissertation Several industries, such as healthcare, manufacturing, and engineering, often encounter scheduling problems that involve the allocation of resources to perform tasks efficiently. The Nurse Rostering Problem is an example of a scheduling problem in healthcare, where nurses are assigned to shifts across a planning period. This talk introduces the use of mathematical optimization tools in solving scheduling problems, specifically, the nurse rostering problem. The structure of a nurse roster is presented along with a mathematical model which defines the constraints and the aim of nurse rostering. This model incorporates several requirements of nurses and hospital management. The performance of exact versus heuristic solution approaches is compared across nurse rosters of various sizes. We also explore the methodology and performance of Variable Neighbourhood Search, a well-known metaheuristic, in improving nurse roster quality to meet nurse and/or hospital preferences. Observers: Stefan Engelhardt and Jacek Gondzio
16:15-16:50	UG1169 Darragh Ferguson Solution Methods for Routing Problems Dissertation Observers: Josh Fogg and Bruce Worton
17:00-17:25	UG1319 Yunyi Cai, Yanqi Chen, Botond Kovag-Laska, Conor Walsh, Yunjia Xiong Hawkes process models in finance Group Project Observers: Josh Fogg and Bruce Worton
17:35-17:55	UG1331 Kinga Bagyo Bounds on the Stability Number of Markov Random Graphs Individual Project Observers: Josh Fogg and Bruce Worton

WEDNESDAY, 27 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 3211
13:10-13:35	UG1298 Yasser Bennadji, Leah Byar, Rosie Matthews, Jessica Smyth Principles of numerical ocean modelling Group Project Observers: Tom Mackay and Max Ruffert
13:45-14:20	UG1302 Oliver Eadie-Catling Building neural networks for diffusive partial differential equations Dissertation Observers: Tom Mackay and Max Ruffert
14:30-14:55	UG1195 Peisheng An, Yexuan Song Voigt wave propagation in anisotropic materials Group Project Observers: Tom Mackay and Max Ruffert
15:10-15:30	UG1134 Matt Gibson Understanding generalisation error and the impact of controlled noise within Gaussian mixture models Individual Project Observers: Miguel de Carvalho and Aretha Teckentrup
15:40-16:15	UG1368 Joshua Jun Leang Ong Detecting Redundancy in the Architecture of Boltzmann Machines Dissertation Observers: Miguel de Carvalho and Aretha Teckentrup
16:25-17:00	UG1358 Anna McElhinney, Lizzie Stansfield, Victoria Sun Modelling metastasis formation Double Group Project Observers: Miguel de Carvalho and Aretha Teckentrup
17:10-17:45	UG1392 Samuel Dauncey Graph-conditioned deep probabilistic modelling Dissertation Observers: Miguel de Carvalho and Aretha Teckentrup

WEDNESDAY, 27 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 4325b
13:10-13:35	UG1258 Runqiu He, Gemma Moss, Yi Ning Tan The Pooling Problem Group Project Observers: Sara Wade and Simon Wood
13:45-14:20	UG1179 Zijie Huang Statistical evaluation of medical tests Dissertation Observers: Sara Wade and Simon Wood
14:30-15:05	UG1185 Guzehong Chen A review of (covariate-dependent) Bayesian mixture models Dissertation Observers: Sara Wade and Simon Wood
15:15-15:40	UG1218 Zonghan Hui, Chenyao Yu, Baoqi Zhang, Weifan Zheng Spatial data analysis for disease mapping Group Project Observers: Sara Wade and Simon Wood
16:00-16:25	UG1229 Tim Xu, Huari Yang, Maiyue Xu Turkey Stock market Dependencies: Study based on wavelet-vine copula approach Group Project This study examines the Turkish stock market (ISE 100) through a Wavelet Vine Copula approach, focusing on dependencies among stock indices from 2005 to 2013 which combines wavelet analysis and vine copula methodology to examine the evolution of market dependence and behaviours across different time intervals, incorporating ARMA-GARCH models to address the dynamic volatility and mean behaviour of stock returns, under different global financial crisis subperiods: pre-crisis(03/01/2005-29/06/2007); crisis(02/07/2007-31/08/2009); and post-crisis(01/09/2009-21/12/2013). Observers: Vanda Inacio De Carvalho and Jordan Richards
16:35-17:10.	UG1287 Feargus Jamieson Ball Statistical Modelling of Extreme Temperatures in the British Isles Dissertation Observers: Vanda Inacio De Carvalho and Jordan Richards
17:20-17:55	UG1339 Axel Eichelmann Modelling Interseasonal Energy Storage Dissertation Observers: Vanda Inacio De Carvalho and Jordan Richards

WEDNESDAY, 27 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 5326
14:10-14:35	UG1273 Ruxandra Icleanu, Dexter Black Patchworking curves Group Project Observers: Pavel Safronov and Vanya Cheltsov
14:45-15:20	UG1388 Mate Gulacsi Classical information theory and applications, II Double Project Observers: Pavel Safronov and Vanya Cheltsov
15:30-15:55	UG1234 Gregor Cochrane, Natalie Goldman, Kotryna Kiznyte, Shiyuan Liu, Hayden Maudsley-Barton Fair division algorithms Group Project Observers: Pavel Safronov and Vanya Cheltsov

WEDNESDAY, 27 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 5327
14:10-14:35	UG1205 Morgan Brougham, Ben Gale, Erin Mill, Emma Puente O'Shea Introduction to inverse problems Group Project In this talk, we introduce the basics of Inverse Problems and how they can be solved using various techniques, with links to linear algebra and statistics. We will use Python to construct our models and illustrate the techniques used. This will be followed by discussion on how these problems can be applied in the real world investigating the mathematics behind medical imaging. Observers: Pieter Blue and Ofer Busani
14:45-15:20	UG1378 Sam Ding Restriced Boltzmann Machines and their Geometry for Classification Dissertation The Restricted Boltzmann Machines (RBMs) is a graphical model which can be interpreted as a stochastic neural network when addressing the classification tasks. This dissertation has a particular focus on the derivation of key formulas and the exploration of their underlying geometric properties. This analysis extends to the practical aspects of training RBMs, employing Gibbs sampling as a critical method for optimizing model performance. Moreover, the dissertation introduces Classification Restricted Boltzmann Machines (ClassRBMs) which is an extension of RBMs, focusing on how they make inferences and applying these theoretical insights to the practical challenge of classifying the MNIST dataset of handwritten digits. Through this rigorous investigation, the dissertation aims to enhance the understanding of RBMs, and indicate their potential as a tool for classification and beyond, while also showing the challenges and intricacies of their training and inference mechanisms. Observers: Pieter Blue and Ofer Busani
15:30-15:55	UG1291 Oleg Lyakh, Tara Moss, Wenhan Zhou, Yuchen Mao, Alex Davis Spatio-Temporal problems using satellite data Group Project Observers: Pieter Blue and Ofer Busani

WEDNESDAY, 27 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 6301
15:10-15:35	UG1246 Amogh Bodas, Matthew Stafford Japanese Temple Mathematics Group Project Observers: David Jordan and Tom Leinster
15:45-16:20	UG1295 Will Spence Topology in Data Science Dissertation Observers: David Jordan and Tom Leinster
16:30-17:05	UG1317 Duncan Thacker Singular Cubic Surfaces Dissertation Motivated by a discussion on the famous 27-line theorem on smooth cubic surfaces, this presentation will lead us to discuss singular cubic surfaces and how lines appear on these surfaces. We will focus our discussion on Du Val singularities and we will describe them through the process of blow-ups. We will then explore previous studies of singular cubic surfaces and move on to the construction of dual graphs. We will finish the presentation with some examples of creating dual graphs from singular cubic surfaces. Observers: David Jordan and Tom Leinster
17:15-17:50	UG1148 Nenna Nwawudu Advanced Topics in Set Theory Dissertation Observers: David Jordan and Tom Leinster

WEDNESDAY, 27 MARCH 2024	MURCHISON HOUSE, ROOM G.09
13:10-13:35	UG1219 Kerem Holland, Phillips Xiao Integrable systems in celestial mechanics Group Project Observers: Clark Barwick and Agata Smoktunowicz
13:45-14:20	UG1303 Carlos Rosuero Set Theory with a Universal Set Dissertation Observers: Clark Barwick and Agata Smoktunowicz
14:30-15:05	UG1125 Alvaro Beattie Eizaguirre Classical information theory and applications Dissertation Observers: Clark Barwick and Agata Smoktunowicz
15:15-15:50	UG1374 Ali Ramsey Bialgebras and Lean Dissertation Lean is a functional programming language which can in particular be used as a proof assistant. We will show how to construct coalgebras and bialgebras - particularly interesting algebraic structures - in Lean. We will then give an overview of the reconstruction theorem for finite-dimensional bialgebras, and discuss the current progress, challenges and possible next steps to formalising this theorem in Lean. Observers: Clark Barwick and Agata Smoktunowicz
16:10-16:45	UG1253 Sophie Bleau The positivity and integrality of mirror maps Dissertation In this talk, we will discuss mirror maps on reflexive polytopes - a recent focal point of mirror symmetry. We will introduce the concept of a reflexive polytope, and apply the mirror map to a simple example of one, which we will refer to throughout the presentation; firstly to familiarise ourselves with the method, but also to recognise the nontriviality of the result. We will build on the proofs by Delaygue on the integrality of the power series given by these maps, and the proofs by Krattenthaler and Rivoal on their positivity, to show that the mirror map power series must have positive integer coefficients for all reflexive polytopes of rank 1. We will also discuss the results of the Sagemath calculations performed on all reflexive polytopes of dimension 2 and 3. Observers: Clark Barwick and Minhyong Kim
17:00-17:25	UG1173 David Aiton, Anna MacIain, Emma O'Dwyer, Otis Parker, Ruoke Wang Mathematics and Music Group Project Observers: Clark Barwick and Minhyong Kim

THURSDAY, 28 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 3212
10:10-10:35	UG1312 Haoyang Wang, Massimo Wu, Rishab Acharya, Tonglu Wang, Yifei Wang Non-Parametric Density Estimation and Regression Group Project This talk delves into Kernel Density Estimation (KDE) and non-parametric regression, highlighting their utility in statistical analysis. Initially, we introduce KDE, discussing its effectiveness through metrics like Mean Squared Error (MSE) and Mean Integrated Squared Error (MISE), alongside asymptotic properties and bandwidth selection strategies such as rule-of-thumb, plug-in methods, and cross-validation. The selection of the Gaussian kernel is emphasized for its broad applicability. Transitioning to non-parametric regression, comparing it to standard regression paradigms, focusing on Nadaraya-Watson, local polynomial regression, and splines. These are appraised based on their performance metrics and the process of selecting smoothing parameters, particularly highlighting the role of leave-one-out cross-validation. Concluding, the project identifies future research directions, including extending KDE to higher dimensions, integrating with machine learning, developing methods for outlier-dense data, and testing on real-world datasets. It advocates for a holistic statistical approach, merging non-parametric techniques with other analytical methods to suit the complex data landscapes of various research domains. Observers: Ozan Evkaya and Konstantinos Zygalakis
10:45-11:10	UG1232 Richard Huang, Callum Purcell Starting journey for Explainable and Responsible Artificial Intelligence: Experiments on Insurance Data Group Project Observers: Ozan Evkaya and Konstantinos Zygalakis
11:20-11:55	UG1285 Estelle McCool Projects in power system reliability Dissertation Observers: Ozan Evkaya and Ioannis Papastathopoulos

THURSDAY, 28 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 4325c
10:10-10:45	UG1297 Hamish Lister Assessing the stability of some clusters of stars Dissertation Observers: Anna Lisa Varri and Konstantina Zerva
11:00-11:35	UG1359 Heidi Berg, Isobel Cox, Caterina Lue Stochastic Models of Cell Populations: Fitting to Interdivision Times Double Group Project Typically, stochastic models of growing cell populations assume that each cell divides after an exponentially distributed period of time. We find that a model with exponentially distributed cell division times well describes the average cell count over time from an experimental dataset of a bacterial cell population but fails to accurately represent the distribution of cell interdivision times. By sup-posing that a cell passes through a series of consecutive stages before dividing, we derive several models with non-Markovian interdivision times that follow the hypoexponential distribution. In particular, we find a model with 3 cell-cycle stages that matches bacterial cell experimental data for interdivision times as well as average cell population count over time. Observers: Anna Lisa Varri and Konstantina Zerva
11:45-12:20	UG1377 Analia Cabello Cano Novel friction-adaptive descent algorithm and its potential applications in machine learning and non-convex optimization Dissertation Observers: Anna Lisa Varri and Konstantina Zerva
12:30-12:50	UG1397 Shuyang Lei Understanding generalisation error in statistical model inference Individual Project Observers: Anna Lisa Varri and Konstantina Zerva

THURSDAY, 28 MARCH 2024	JAMES CLERK MAXWELL BUILDING, ROOM 5205
10:10-10:35	UG1228 Joseph Muldoon, Samuel Webb, Timothy Harvey Proving mathematical theorems in LEAN Group Project Observers: Tudor Dimofte and Sjoerd Beentjes
10:45-11:20	UG1268 Adam Rafferty The geometry of magnetic monopoles Dissertation Observers: Tudor Dimofte and Sjoerd Beentjes
11:30-12:05	UG1357 Adam Lofthouse Condensed/pyknotic mathematics Dissertation Observers: Tudor Dimofte and Sjoerd Beentjes