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              <text>Factorising integers using elliptic curves</text>
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              <text>Mathematics, Elliptic curves</text>
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                <text>Factorising integers using elliptic curves</text>
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                <text>Mathematics</text>
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                <text>2026</text>
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                <text>Hamza Zahid</text>
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              <text>This project studies the weak and strong cop numbers of Cayley graphs of finitely generated groups, with particular emphasis on methods for proving that the strong cop number is infinite. After reviewing several known results and techniques, we investigate a number of non-hyperbolic examples. For right-angled Artin groups, we use quasi-retractions onto Z² to determine their strong cop numbers in the non-free case. A novelty of this work is the proof that the discrete three-dimensional Heisenberg group H₃(Z) has infinite strong cop number. To show this, we introduce a weighted coordinate function comparable to the word metric and use the natural Heisenberg dilations to construct a sequence of quasi-homotheties. Motivated by this argument, we study a semidirect product Z³ ⋊ₐ Z and establish an analogous word-metric comparison, while the corresponding quasi-homothety problem is left open.</text>
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              <text>geometric group theory, cops and robbers, strong cop number, weak cop number, Cayley graphs, Heisenberg group, quasi-homothety, right-angled Artin groups</text>
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                <text>Infinite Strong Cop Number of the Three-Dimensional Heisenberg Group</text>
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                <text>Geometric group theory and coarse cops and robbers on Cayley graphs</text>
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            <name>Date</name>
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                <text>September 2026</text>
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                <text>Dr Jerónimo García Mejía (URSS Supervisor)</text>
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              <text>The Russia--Ukraine war disrupted global food commodity markets, raising concerns over food prices and food security across Africa. This study examines whether countries with greater pre-war dependence on cereal imports from Russia and Ukraine experienced larger increases in domestic food inflation following the outbreak of the conflict, and whether transmission varied with economic development.  Using a monthly panel of 25 African economies from January 2017 to September 2025, the study employs a Difference-in-Differences framework exploiting cross-country variation in pre-war import dependence. Country and month fixed effects account for unobserved heterogeneity and common global shocks, while exchange-rate movements are included as a control. Robustness is assessed using alternative treatment definitions, fixed-effects specifications, placebo tests and leave-one-country-out estimation.  The baseline results provide limited evidence that pre-war dependence on Russian and Ukrainian cereal imports systematically increased domestic food inflation following the outbreak of the war. However, substantial heterogeneity emerges across countries. Higher economic development is associated with significantly smaller increases in food inflation. Further analysis indicates that supplier concentration and domestic cereal production capacity help explain this resilience. Overall, the findings suggest that structural characteristics, rather than import dependence alone, shape countries' resilience to global food commodity shocks.</text>
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              <text>Economics, Food inflation, Food prices, Commodity price shocks, Russia-Ukraine war, Africa, Economic development, Food security, Cereal imports, Import dependence, Economic resilience, Difference-in-Differences, International economics</text>
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                <text>The Transmission of Global Food Commodity Shocks to Food Inflation in Africa: Evidence from the Russia–Ukraine War</text>
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                <text>International Economics / Development Economics - Food Prices, Commodity Shocks and Economic Resilience</text>
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            <name>Date</name>
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                <text>Jun-Aug 2026</text>
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                <text>Daniel Whitehouse, Prof Natalie Chen</text>
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              <text>Fraudulent banking transactions create substantial financial and operational risks for financial institutions and their customers. The increasing availability of transaction-level data provides an opportunity to identify potentially fraudulent activity using statistical learning methods. This study aims to develop and compare statistical models for predicting whether a banking transaction is fraudulent. A labelled dataset containing approximately 200,000 transaction records is used, with fraud status represented by the binary response variable Fraud. After the removal of direct personal identifiers and other unsuitable fields, variables describing transaction characteristics, customer information, account balances, merchant categories, locations and transaction devices are considered as potential predictors.  The labelled data are divided into a 70% training set and a 30% test set using stratified sampling. Two multiple logistic regression models are developed using different sets or representations of the predictor variables. For each model, backward stepwise selection based on the Akaike Information Criterion is used to reduce the full set of candidate predictors. Five-fold cross-validation is conducted within the training data to examine the predictive performance of the modelling procedures. The two final models are then fitted using the complete training set and applied to the independent test set.  The test predictions are compared with the actual fraud outcomes using confusion matrices, and the predictive accuracy of each model is calculated. Model 1 achieved a test accuracy of 96.91%, while Model 2 achieved a slightly higher accuracy of 96.93%. Therefore, Model 2 was selected as the final model based on its higher test accuracy. The findings demonstrate how logistic regression and backward variable selection can be used to support the identification of potentially fraudulent banking transactions. However, the results should be interpreted considering limitations relating to data quality and the possible use of simulated transaction data.</text>
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              <text>fraud detection, banking transactions, logistic regression, statistical modelling, R</text>
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                <text>Fraud detection in bank transactions using statistical modelling</text>
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                <text>Fraud detection in bank transactions </text>
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                <text>2026-09-26</text>
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                <text>Lisa Li</text>
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              <text>This paper discusses the polity of the Norman adventurer Roussel de Bailleul which existed between 1073 and 1075. It answers how the polity survived for nearly two years with the use of a 'Norman Frontier Society Model' which was similar to other Norman polities such as the Kingdom of Sicily and the Principality of Antioch. Alongside this model, primary sources are utilised to create a contextualised picture of this polity in terms of its politics, economy and society.</text>
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                <text>The Normans in Anatolia: An Analysis of the Functioning of the Polity of Roussel de Bailleul during the 1070s</text>
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                <text>Byzantine Anatolia during the 1070s, primarily the polity of Roussel de Bailleul</text>
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                <text>1073-1075</text>
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                <text>Aysu Dincer Hadjianastasis</text>
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              <text>This project investigates digit phenomena motivated by a question of Paul Erdős. We study the occurrence of the digit 7 in powers of 2, asking whether every sufficiently large power of 2 contains the digit 7. More generally, we consider the sequence (a·2ⁿ) for varying positive integers a and formulate the following conjecture: the set of a for which a·2ⁿ contains the digit 7 for all sufficiently large n has full natural density. In pursuit of this conjecture, we develop useful combinatorial and arithmetic estimates, together with a dynamical approach to the leading digits of these numbers.</text>
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              <text>number theory, digit occurrence, powers of two, geometric progressions, Benford's law, natural density, logarithmic density, dynamical systems, shrinking targets, irrational rotations, combinatorics, Erdős</text>
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                <text>Digit Occurrence in Geometric Progressions</text>
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                <text>Mathematics – Number Theory and Dynamical Systems</text>
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                <text>21/09/2026</text>
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                <text>Joel Moreira</text>
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              <text>This project showcases the packing of circles and ellipses using conic shapes and focal conics. We derive Descartes’ equation and an equivalent of it in hyperbolic space, then go over an application within a liquid crystal and derive the cylcides of Dupin that are around a given focal conic.</text>
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              <text>Physics, Theoretical physics, Mathematics, Geometry</text>
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                <text>Focal Conics: From Number Theory to Materials Geometry</text>
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                <text>Dr. Gareth Alexander</text>
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              <text>This project gives an introduction to the Jacobian of smooth algebraic curves, giving three separate constructions. We then survey the theory for nodal algebraic curves and give a worked example.</text>
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              <text>Algebraic Geometry</text>
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                <text>The Jacobian of Non-Smooth Algebraic Curves</text>
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                <text>Mathematics</text>
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                <text>2026</text>
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              <text>This project investigates calibration methods for an ultrasonic anemometer affected by receiver-positioning error and differences in the dynamic response of flexural ultrasonic transducers (FUTs). Receiver positioning produces both a zero-flow timing offset and a residual flow-dependent error that cannot be removed by zero-flow calibration alone. A combined calibration procedure is developed in which the temperature-dependent FUT response is first characterised, followed by zero-flow calibration and known-flow calibration to determine the remaining positioning response. A mass–spring–damper model is used to relate FUT ring-down behaviour to the steady-state phase during continuous-wave operation. Numerical simulations show that the proposed calibration can recover the flow velocity with very small residual error under the assumed models. The positioning-error calibration is derived from the existing receiver-positioning model, while the proposed FUT phase correction remains to be experimentally validated.</text>
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              <text>ultrasonic anemometry, ultrasonic sensing, calibration, flexural ultrasonic transducers, FUT, flow measurement, positioning error, zero-flow offset, transit-time difference, temperature compensation, phase response, numerical modelling</text>
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                <text>Jacky So</text>
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              <text>This project explores the causes and lasting consequences of European immigration to Argentina. It begins by considering the historical context of European emigration, including economic hardship, political instability, war, and persecution, alongside the factors that made Argentina an attractive destination, such as its expanding economy, immigration-friendly policies, and abundance of fertile land. It then examines the diverse groups who settled in Argentina and assesses how they reshaped the country's language and culture. Finally, it reflects on the continuing legacy of this migration, considering both personal observations from my visit to Argentina and the ways in which immigration to the country has evolved in the present day.</text>
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              <text>Argentina, History, Immigration, Emmigration, Migration, History of Immigration, History of South America, Linguistics, Culture, Hispanic Culture, History of Linguistics, Spanish, History of the Spanish Language </text>
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                <text>The Sociolinguistic Impact of Immigration on Argentina</text>
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                <text>Amelia Brady</text>
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