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              <text>This project report explores the base sizes of group actions. We begin with some preliminary definitions and results. Next, we investigate a combinatorial approach to proving the bound $|G| \geq 2^{b(G)}$; we give a conjecture for a stronger statement concerning a system of distinct representatives for sets $\left\{ \bigcap\limits_{\alpha \in \Omega}\mathrm{Stab}_G(\alpha) : \emptyset \neq \Omega \subseteq B \right\}$, where $B$ is a minimal base for a permutation group $G$.  Subsequently, we follow a paper of Burness, O'Brien and Wilson in explaining various computational and character-theoretic techniques that can be used to compute base sizes. Finally, we apply these methods to a selection of almost simple sporadic groups and their subgroups.</text>
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              <text>This research report examines the mining industry in Guatemala, focusing on the diverse perspectives of various stakeholders regarding development and the industry’s benefits. Through a series of interviews with indigenous community members, government officials, and academics, the study explores the multifaceted impacts of mining activities. The findings reveal a complex landscape where economic benefits, such as job creation and infrastructure development, are weighed against environmental degradation and social disruption. Indigenous community members express concerns about health risks and loss of traditional livelihoods, while academics highlight economic growth and technological advancements. Government officials discuss regulatory challenges and policy implications, emphasizing sustainable long-term practices. This report aims to provide a comprehensive understanding of how the mining industry aligns with or contradicts the development goals of different stakeholders, offering insights for policymakers to balance economic and social interests.</text>
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              <text>Once a porous material becomes contaminated with a chemical agent the typical solution is to introduce a cleansing fluid to the surface of the material, allowing the cleanser to react with the agent and creating a less harmful product which neutralises the solution and decontaminates the material. Usually the cleanser and the agent are insoluble, so a flat boundary between the two solutions develops where the decontamination reaction occurs, which moves down through the material over time. We introduce a decay reaction between the cleansing fluid and the porous material to an existing model, and investigate the impact this has on the decontamination process. We shall show for systems with sufficiently large decay that the decontamination efficiency loses its dependence on cleanser strength, meaning that unlike low decay systems there is no drawback to using a weaker cleanser.</text>
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                <text>A personal blog where I discuss my experience of working in a Neuroscience laboratory, undergoing a project studying the stress-induced gene expression changes in the NTS.</text>
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