title: Iwasawa theory for tensor products of Hilbert modular forms

authors: Corpuz, Raiza

abstract: 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.

text: Iwasawa theory for tensor products of Hilbert modular forms 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.

year: 2025

title: David Bowie and the Art of Music Video

authors: Perrott, Lisa

subjects: Art

abstract: The first in-depth study of David Bowie's music videos across a sustained period takes on interweaving storyworlds of an iconic career. Remarkable for their capacity to conjure elaborate imagery, Bowie's videos provide fascinating exemplars of the artistry and remediation of music video. When their construction is examined across several years, they appear as time-travelling vessels, transporting kooky characters and strange story-world components across time and space. By charting Bowie's creative and collaborative process across five distinct phases, David Bowie and the Art of Music Video shows how he played a vital role in establishing music video as an artform. Filling a gap in the existing literature, this book shines a light on the significant contributions of directors such as Mick Rock, Stanley Dorfman and David Mallet, each of whom taught Bowie much about how to use the form. By examining Bowie's collaborative process, his use of surrealist strategies and his integration of avant-garde art with popular music and media, the book provides a history of music video in relation to the broader fields of audiovisual media, visual music and art.

text: David Bowie and the Art of Music Video The first in-depth study of David Bowie's music videos across a sustained period takes on interweaving storyworlds of an iconic career. Remarkable for their capacity to conjure elaborate imagery, Bowie's videos provide fascinating exemplars of the artistry and remediation of music video. When their construction is examined across several years, they appear as time-travelling vessels, transporting kooky characters and strange story-world components across time and space. By charting Bowie's creative and collaborative process across five distinct phases, David Bowie and the Art of Music Video shows how he played a vital role in establishing music video as an artform. Filling a gap in the existing literature, this book shines a light on the significant contributions of directors such as Mick Rock, Stanley Dorfman and David Mallet, each of whom taught Bowie much about how to use the form. By examining Bowie's collaborative process, his use of surrealist strategies and his integration of avant-garde art with popular music and media, the book provides a history of music video in relation to the broader fields of audiovisual media, visual music and art.

year: 2023-07-27

title: Angitūtanga o ngā tauira Māori:  Supporting Māori students to succeed in psychology

authors: Martin, Dionne

subjects: Psychology

abstract: Many Māori seek out university degrees to make a meaningful impact on the health of their community. Psychology, is one avenue that attracts Māori to do so. Psychology training has often failed to meet the needs of Māori students, often creating barriers to Māori student success. This thesis will explore barriers and support mechanisms that Māori students experience while attending university in pursuit of psychology degrees. This study will focus on experiences had by those enrolled in The School of Psychology at The Univeristy of Waikato, on the Hamilton campus. Informed by kaupapa Māori guidelines and analysed though the use of pūrākau this thesis highlights some key experiences shared by Māori psychology students. Three key experiences were identified. First, the prominence of Western culture in The School of psychology and the impact that has on Māori sense of belonging and whanaungatanga. Second, support system realities for Māori, identifying key university supports systems and realities associated with ones home environment. Third, the transitional journey to becoming a psychologist and what impact that has on the university journey. With this in mind, some recommendations are made to support Māori student success in psychology. These recommendations advocate for the provision of a more bicultural learning experience, creation of a culturally affirming environment, recruitment and retention of culturally capable staff, appropriate resourcing, funding and training for support services, better support for Māori realities and pathway navigation support.

text: Angitūtanga o ngā tauira Māori:  Supporting Māori students to succeed in psychology Many Māori seek out university degrees to make a meaningful impact on the health of their community. Psychology, is one avenue that attracts Māori to do so. Psychology training has often failed to meet the needs of Māori students, often creating barriers to Māori student success. This thesis will explore barriers and support mechanisms that Māori students experience while attending university in pursuit of psychology degrees. This study will focus on experiences had by those enrolled in The School of Psychology at The Univeristy of Waikato, on the Hamilton campus. Informed by kaupapa Māori guidelines and analysed though the use of pūrākau this thesis highlights some key experiences shared by Māori psychology students. Three key experiences were identified. First, the prominence of Western culture in The School of psychology and the impact that has on Māori sense of belonging and whanaungatanga. Second, support system realities for Māori, identifying key university supports systems and realities associated with ones home environment. Third, the transitional journey to becoming a psychologist and what impact that has on the university journey. With this in mind, some recommendations are made to support Māori student success in psychology. These recommendations advocate for the provision of a more bicultural learning experience, creation of a culturally affirming environment, recruitment and retention of culturally capable staff, appropriate resourcing, funding and training for support services, better support for Māori realities and pathway navigation support.

year: 2025