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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>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>Marco Fava</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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              <text>An educational article introducing the weak topology, and compactness results in L^p spaces. </text>
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              <text>pure mathematics, functional analysis, weak convergence, weak topology, young measures</text>
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                <text>Ewelina Zatorska</text>
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              <text>Professor Alexander Dobson</text>
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              <text>This study investigates the relationship between urban slum populations and key economic indicators across districts in Karnataka, integrating behavioural economics insights into conventional regression analysis. Using district-level data on Gross District Domestic Product (GDDP), Per Capita Income (PCI), and slum populations, an Ordinary Least Squares (OLS) regression model was estimated to examine the economic determinants of slum persistence. The model explains approximately 67.7% of the variation in slum populations (R² = 0.677) and reveals a statistically significant positive association between GDDP and slum population.</text>
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                <text>Behavioural Barriers and growth of slums in Urban Karnataka</text>
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                <text>Anirudh Nagaraj</text>
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              <text>This study examines the impact of the Pradhan Mantri MUDRA Yojana (PMMY) on enterprise creation in India, addressing a gap in the literature that emphasises loan trends rather than causal outcomes. Using panel data from 33 states and union territories between 2011–2021, fixed-effects regressions estimate the relationship between per-capita PMMY disbursements and MSME registrations. The results show a marked rise in MSME formation after the scheme’s launch in 2015, with per-capita lending associated with nearly one additional MSME per 1,000 people in the following year. This relationship remains robust after controlling for income, banking infrastructure and national shocks, though significant variation exists across states. Wealthier states display stronger impacts, while poorer or infrastructure-constrained regions benefit less. Interviews with beneficiaries support these patterns, indicating that although PMMY improves credit access, sustained enterprise growth also depends on market access, financial literacy and broader institutional support. </text>
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                <text>Does Microfinance Drive Entrepreneurship? Evidence from India’s Microfinance Scheme (PMMY)</text>
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                <text>Aayush Bhandari</text>
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              <text>We prove a weaker version of the Diophantine property for the automorphism group of an infinite regular rooted tree of degree $d\geq 3$. </text>
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                <text>Timucin Oisin Gunaydin</text>
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              <text>This paper examines how central banks integrating sustainability initiatives into monetary policy affects macroeconomic stability. Using quarterly data for 184 countries from 2001 to 2024, we assess whether membership in the Network for Greening the Financial System (NGFS), as a proxy to show whether a central bank is sustainable, influences five macroeconomic variables: inflation, inflation volatility, GDP growth, GDP volatility, and unemployment. A series of pooled OLS and fixed effects regressions are used, while semi-structured interviews with central bank officials complement the quantitative analysis. The results indicate that NGFS membership is generally associated with greater macroeconomic stability in high-income economies, reflected in lower inflation, stronger growth, and reduced volatility. Interviewees from high- and middle-income countries agreed that their central banks did not recognise a trade-off between sustainability in central banking, and the effectiveness of monetary policy. However, regression results indicate that middle- and low-income countries experience trade-offs, possibly due to weaker institutional capacity and resource constraints.</text>
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                <text>How Effective is Monetary Policy for Macroeconomic Stabilisation when Environmental Sustainability is a Central Bank Objective?</text>
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                <text>How Effective is Monetary Policy for Macroeconomic Stabilisation when Environmental Sustainability is a Central Bank Objective?</text>
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                <text>Soham Warikoo and Monisha Pandhi</text>
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              <text>With the rise and growing influence of what has been called ‘populist’ leaders and ideas, the concept of populism has gained significant relevance in recent years, both in academic and public discourse. Alongside this trend, anti-populism has emerged as a strong counterforce, critiquing the rise of populism and populist ideas. Scholars have shown that anti-populism, empowered through dominant public and media discourses on populism, has been a powerful lens through which to define the concept of populism itself. The latter has become increasingly misunderstood as a danger to democracy, while there in fact exist a variety of populisms, left- and right-wing, democratic and anti-democratic. This research project will therefore explore the difficulties associated with defining both populism and anti-populism as concepts and investigate the democratic potential of left-wing populist movements that have developed in response to democratic crises. Finally, I will explore how the media engages with populist ideas, figures and parties. This will include a focus on how the written media practises agenda-setting and deflection when discussing populism, as well as the role of populist hype in the euphemisation, trivialisation and amplification of populism through The Guardian’s articles.</text>
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                <text>Politics and International Studies </text>
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                <text>Eliana Judd</text>
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                <text>Populism, Anti-populism, and Democracy: Rethinking Dominant Discourses on Populism</text>
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