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Iwasawa theory for tensor products of Hilbert modular forms
(The University of Waikato, 2025) Corpuz, Raiza; Delbourgo, Daniel; Lei, Antonio; Stokes, Tim
The main conjecture of Iwasawa theory bridges two seemingly disjoint areas of mathematics: arithmetic and analysis. In particular, it provides a deep connection between the p-adic L-function which interpolates critical values of the complex L-series, and the Selmer group which is an important object used to control the growth of arithmetic data. In this thesis, we explore some questions that arise organically from the Iwasawa Main Conjecture, applied to Hilbert modular forms and their tensor products. Greenberg and Vatsal developed an approach to study the main conjecture for a large class of elliptic curves simultaneously. They showed that if a given pair of elliptic curves share the same residual Galois representation, then the main conjecture holds for one if and only if it does for the other. The first part of this thesis investigates whether the ideas of Greenberg and Vatsal work for elliptic curves twisted by a CM-Hecke character. The second part of this thesis then extends the method to treat non-ordinary classical modular forms (without any twist). The former permits one to study rational elliptic curves base-changed to an arbitrary number field, whilst the latter requires techniques crafted by Pollack and Kobayashi in the early 2000s. Finally, the third part of this thesis concerns Euler systems and their applications to the arithmetic of motives arising from modular forms—these objects are indispensable tools which can be used to prove half of the Iwasawa main conjecture. However they often give rise to additional “junk” error terms, as well as causing the p-adic L-function to be stripped away of certain bad Euler factors. For modular forms and their tensor products we devise a method to dispose of the error terms and to replenish the missing factors, allowing one to genuinely obtain half of the main conjecture free from any discrepancies.
The structural and mechanistic characterisation of Thermophilic RNA Ligases
(The University of Waikato, 2025-09-14) Kamal, Aliyah; Hicks, Joanna
MicroRNAs (miRNAs) are short regulatory RNAs that play critical roles in post-transcriptional gene regulation. Dysregulation of miRNA expression can be implicated in numerous diseases, including cancer, making miRNAs valuable diagnostic and prognostic biomarkers. Next-generation sequencing (NGS) enables quantitative profiling of miRNA populations, but a key limitation lies in the adapter ligation step required for library preparation. Current commercial RNA ligases, typically active between 14-37 ℃, display strong biases based on RNA sequence and secondary structure resulting in a skewed representation of miRNA populations. At low temperatures, miRNA secondary structures can obscure 5’-phosphate, and 3’-hydroxyl ends, preventing efficient ligation. Thermophilic RNA ligases with high thermostability and distinct substrate preferences may therefore reduce ligation bias and improve NGS accuracy. The archaeal Paleococcus pacificus RNA ligase (PpaRnl) represents a valuable model for exploring the structural and mechanistic features of thermophilic RNA ligases. This study aimed to further investigate the substrate preference of a PpaRnl mutant; K238G, a point mutation of lysine at position 238, a key residue in the coordination of the AMP and in turn the binding of the Mg2+ ions in PpaRnl. Alongside the structural and mechanistic characterisation of several PpaRnl mutants to explore the role of a newly identified Mg2+ binding site (Mg2+ B) close to the active site. Key residues for coordinating the Mg2+B ion were mutated in the PpaRnl enzyme (D94A, D248A, E155A, and the double mutant D94A-D248A) as characterisation of these mutants would allow for a deeper understanding of this mechanism. Mutants were expressed in Escherichia coli and purified using a combination of immobilised metal affinity chromatography (IMAC) and gel-filtration chromatography. Expression and purification outcomes varied significantly between constructs, while some mutants were successfully obtained in sufficient yields, others demonstrated poor or inconsistent expression, often not even seeing improvement after optimisation of growth conditions and large-scale culture volumes. In particular, the E155A mutant displayed extremely slow growth, while the D94A-D248A double mutant produced negligible results across expression trials. Further characterisation of the mutants, K238G, D94A, and D248A, had shown that these enzymes retain robust activity between 60-65 ℃, with measurable activity extending up to 80 ℃. Distinct sequence and cofactor preferences were observed. When combined with adapters, these mutants efficiently produced RNA ligation products with minimal side reactions and, in several cases, displayed improved activity compared to the wild-type enzyme. The structures of PpaRnl D94A and D248A were solved via X-ray crystallography and although there was similarity in the structures compared to that of the wild-type enzyme and K238G, it was found that a number of the residues coordinating the ligands present within the active-site had changed their orientation. This resulted in the Mg2+B ion not being present in D94A, and no AMP cofactor, Mg2+A or Mg2+B present within the D248A mutant. Overall, this work highlighted the variability in expression and crystallisation outcomes among the second Mg2+ binding site mutants of PpaRnl with notable differences observed in expression, activity, and structure, highlighting that the Mg2+B ion and its coordination have an impact of the efficiency of the enzyme. This unique mechanism is still not fully understood but its importance and impact has been highlighted within this research, reiterating the importance of construct specific optimisation in structural studies and the potential utility of engineered thermophilic RNA ligases, as tools to reduce ligation bias in NGS based miRNA sequencing. Allowing for the possible discovery of biomarkers within viral diseases, and cancer.
A sustainable solution for nitrate pollution in New Zealand's drinking water capacitive deionization (CDI)
(The University of Waikato, 2026-01-27) Sharma , Anisha; Mark, Lay
Abstract This study investigates the performance, feasibility, and practical implications of a small-scale Capacitive Deionization (CDI) system for simultaneous NaCl and Na₂NO₃ removal from water, focusing on rural and agricultural applications in New Zealand. Seven trials were conducted under varying ionic loads, flow rates, and voltages, with operational parameters and removal efficiencies recorded. Conductivity and nitrate concentration trends were closely monitored, revealing high nitrate removal rates (up to 79.8%) and significant conductivity reduction across multiple cycles. The system demonstrated stable adsorption–desorption patterns, with minimal fouling and rapid regeneration. Comparative cost analysis with Reverse Osmosis (RO) and Ion Exchange indicated CDI’s substantial economic advantage, with a cost per litre of 0.61 cents, over five times lower than RO, combined with reduced energy consumption (1.97 NZD/year). Beyond water treatment, the recovered nitrate stream presents an opportunity for agricultural reuse, reducing nitrogen fertilizer costs and contributing to nutrient recycling. The results confirm CDI’s adaptability for low-resource settings, offering a low-maintenance, scalable, and environmentally sustainable alternative for decentralized water treatment. Furthermore, derived performance metrics highlighted consistent removal efficiency even under varying salinity conditions, supporting its resilience for fluctuating feedwater qualities common in rural supplies. Integrating CDI into farm-level water management could enhance water quality and soil nutrient availability, supporting sustainable farming practices. Future research should focus on long-term field trials, optimization of electrode materials for mixed-ion selectivity, and system integration with renewable energy sources to further reduce operating costs and environmental impact.
Subcanopy responses to human-induced disturbances: Astrolabe/Otāiti and Motiti Reefs under the MV Rena and climate change stressors
(The University of Waikato, 2026-01-27) Elizabeth , Thompson; Battershill, Chris
Disturbances are recognised as key drivers of ecosystem change, yet there remains limited consensus on how different disturbance types interact, particularly across trophic levels and within subcanopy communities. Existing theories often overlook the nonlinear relationships between climate-driven stressors and species interactions, underscoring the need for system-specific studies to clarify recovery mechanisms. The grounding of the MV Rena on Astrolabe Reef/Otāiti in 2011 resulted in New Zealand’s worst maritime environmental disaster. Fourteen years later, this provides a rare opportunity to assess how legacy disturbance interacts with natural variability to influence subcanopy assemblages. This thesis investigated subcanopy dynamics at two Bay of Plenty locations: Astrolabe Reef, directly impacted by the MV Rena wreck, and Motiti Island, a nearby reef indirectly affected by the wreck, but directly affected by Cyclone Gabrielle, and both systems subject to fishing pressure, sedimentation, and other stressors. Biodiversity surveys, species inventories and Baited Remote Underwater Videos, were combined with manipulative clearance experiments to test environmental responses. At Astrolabe Reef, small-scale clearances were established in high and low impact zones, while at Motiti Island, large canopy removals in Carpophyllum spp and Ecklonia radiata transition zones simulated storm-driven disturbance. Quantitative assessments after eleven weeks of the clearances revealed rapid recolonisation but divergent trajectories. At Astrolabe Reef, sites nearer the wreck were dominated by turfing algae and urchins (Centrostephanus rodgersii), while more distant sites supported greater sponge richness and habitat heterogeneity. At Motiti Island, opportunists such as kina (Evechinus chloroticus) and turfing algae shifted into available space. Carpophyllum spp. recovered strongly and expanded downslope, contrasting with the weak recovery of Ecklonia radiata. These findings demonstrate that outward canopy recovery can mask deeper structural shifts in subcanopy communities. More broadly, they highlight how legacy disturbance, grazer dynamics, and climate-driven pressures interact to shape resilience pathways in temperate reefs.
Taonga maioha: (Born this way) The in-depth stories of three Māori, Pasifika, and Indigenous Queens
(The University of Waikato, 2024) Tamuera Ariki, Paikea
Who else has the right to define these, Queens? This thesis provides a vital platform for the voices of three Māori, Pasifika, and Indigenous Queens, allowing them to share their transformation stories in their own words. Their experiences and feelings about in their words “being born into the wrong bodies” highlight the complex realities of identity and the struggle for acceptance by others. These Queens are unified in their desire for dignity and respect. Dignity and respect underscore a fundamental human right. They seek recognition in all areas of their lives, from healthcare to education, housing, employment, and beyond. By articulating their needs, they advocate for themselves and all marginalized individuals, seeking fairness and understanding within systems that often overlook them. Focusing on their lived experiences is crucial for fostering empathy and promoting systemic change, as it brings attention to the disparities they face and the importance of inclusivity in society. By sharing their truths, these Queens contribute to a broader dialogue about identity, respect, and the pursuit of equality for all. This thesis aims to illuminate the transformation stories or pūrākau of ten Māori and Pasifika Queens, to foster understanding of their unique experiences. The focus on those who identify as wahine despite being born biologically male allows the reader to highlight the rich diversity of gender identity within these cultures and groups. The Māori Ethics Committee granted ethics approval for the study, thereby paving the way for the Queens to tell their stories or pūrākau from their truths and perspectives. Taonga Maioha details the in-depth transformation stories of three Māori-Pasifika Queens aged 60 plus, supported by a contextual and cultural analysis of their generation. The voices and stories of the Queens are central to this thesis. These stories are thematically analyzed to unpack the cultural and generational influences impacting their identities. The core identity constructs of whakapapa, tinana, hinengaro, and wairua are used to frame and organize their transformation stories according to their instructions. Above all, this thesis is anchored in their rights to define themselves on the premise that they have the mana to define themselves irrespective of others who define them from the sidelines of their lives. Their definitions are theirs alone. The storytellers call themselves Queen, Wahine, or women. This is based on the assertion that it is their right to be called a Queen. In certain contexts, they may refer to themselves as takatāpui and transgender for the sake of acceptance by others. This thesis is written to enhance the mana of the storytellers. These are their stories and their truths. The late Dame Georgina Beyer, was one of the original participants in this thesis. Many interviews were conducted with her. Instructed by Georgina before her passing to publish elements of her story as part of this thesis. Unfortunately, the Ethics Committee at Waikato University did not accept this due to her passing. Hence, the reason ‘First Lady’ was introduced, where Liz Roberts gives exclusive details of her change, both legally and physically.