title: Iwasawa theory over solvable three-dimensional p-adic Lie extensions

authors: Qin, Chao

subjects: Iwasawa theory

abstract: Iwasawa theory is a powerful tool which describes the mysterious relationship between arithmetic objects (motives) and the special values of L-functions. A precise form of this relationship is neatly encoded in the so-called "Iwasawa Main Conjecture". Classically the Main Conjecture (as formulated by Iwasawa himself) involved the behaviour of ideal class groups over cyclotomic Zp-extensions, and related this to the Kubota-Leopoldt p-adic zeta-function. During the last two decades, the main conjecture has been greatly generalized to admissible p-adic Lie extensions, and provides a conjectural relationship between L-values of motives and their associated Selmer groups. A key component of the “Non-commutative Iwasawa Main Conjecture” in [CFK+05] predicts the existence of an analytic p-adic L-function L an M inside K1 ( Zp[[G∞]]S∗ ) . To establish the existence of such an object, we need to be able to do two things: (1) describe K1 ( Zp[[G∞]]S∗ ) in terms of the Artin representations factoring through G∞ using p-adic congruences, and then (2) show for each motive that the abelian fragments satisfy these congruences. This thesis provides a complete answer to the first task (1), in the specific situation where the pro-p-group G∞ has dimension ≤ 3 and is torsion-free. We completely describe K1(Zp[[G∞]]) and its localisations by using an infinite family of p-adic congruences, where G∞ is any solvable p-adic Lie group of dimension 3. This builds on earlier work of Kato when dim(G∞) = 2, and of Daniel Delbourgo and Lloyd Peters when G∞ ∼= Z × p ⋉Zd p with a scalar action of Z × p . The method exploits the classification of 3-dimensional p-adic Lie groups due to González-Sánchez and Klopsch, as well as the fundamental ideas of Kakde, Burns, etc. in non-commutative Iwasawa theory. We also undertake a short study of elliptic curves over GL2(Fp)-extensions, and compile some numerical evidence in support of the first layer congruences predicted by Kakde [Kak17] for non-CM curves.

text: Iwasawa theory over solvable three-dimensional p-adic Lie extensions Iwasawa theory is a powerful tool which describes the mysterious relationship between arithmetic objects (motives) and the special values of L-functions. A precise form of this relationship is neatly encoded in the so-called "Iwasawa Main Conjecture". Classically the Main Conjecture (as formulated by Iwasawa himself) involved the behaviour of ideal class groups over cyclotomic Zp-extensions, and related this to the Kubota-Leopoldt p-adic zeta-function. During the last two decades, the main conjecture has been greatly generalized to admissible p-adic Lie extensions, and provides a conjectural relationship between L-values of motives and their associated Selmer groups. A key component of the “Non-commutative Iwasawa Main Conjecture” in [CFK+05] predicts the existence of an analytic p-adic L-function L an M inside K1 ( Zp[[G∞]]S∗ ) . To establish the existence of such an object, we need to be able to do two things: (1) describe K1 ( Zp[[G∞]]S∗ ) in terms of the Artin representations factoring through G∞ using p-adic congruences, and then (2) show for each motive that the abelian fragments satisfy these congruences. This thesis provides a complete answer to the first task (1), in the specific situation where the pro-p-group G∞ has dimension ≤ 3 and is torsion-free. We completely describe K1(Zp[[G∞]]) and its localisations by using an infinite family of p-adic congruences, where G∞ is any solvable p-adic Lie group of dimension 3. This builds on earlier work of Kato when dim(G∞) = 2, and of Daniel Delbourgo and Lloyd Peters when G∞ ∼= Z × p ⋉Zd p with a scalar action of Z × p . The method exploits the classification of 3-dimensional p-adic Lie groups due to González-Sánchez and Klopsch, as well as the fundamental ideas of Kakde, Burns, etc. in non-commutative Iwasawa theory. We also undertake a short study of elliptic curves over GL2(Fp)-extensions, and compile some numerical evidence in support of the first layer congruences predicted by Kakde [Kak17] for non-CM curves.

year: 2018

title: Fractional behaviour of rechargeable batteries

authors: Hasan, Rahat

abstract: For decades authors have preferred to model batteries with either Thevenin-style models using RLC, or Randlesstyle by adding a Warburg element. These are claimed to model accurately. We present convincing empirical evidence suggesting that a fractional-derivative (constant-phase element) model is required. Our data shows that existing state-of-the-art models may be overly complicated, requiring numerical rather than physical considerations to find parameters.

text: Fractional behaviour of rechargeable batteries For decades authors have preferred to model batteries with either Thevenin-style models using RLC, or Randlesstyle by adding a Warburg element. These are claimed to model accurately. We present convincing empirical evidence suggesting that a fractional-derivative (constant-phase element) model is required. Our data shows that existing state-of-the-art models may be overly complicated, requiring numerical rather than physical considerations to find parameters.

year: 2016

title: Spill-over of sustainability values and practices - a psychology PhD thesis proposal

authors: Rua, Mohi

subjects: Maori

abstract: The following presentation relates to my proposed PhD topic. As an audience you’re probably reading the title and wondering what relevance my topic has to the symposium theme Claiming Spaces. My immediate response is ‘nothing’. Nada, zilch, kore. As a ‘fill-in’ speaker for a presenter unable to be here, I’m reminded that despite my topics irregularity in the programme, I claim a space as both a psychologist and Maori person seeking to work with in the field of sustainability and conservation. Psychologists and Maori are interested in more than mental health and clinical investigation. We are interested in how the world goes around and seek to claim a space here too. So, this symposium and my participation DOES have relevance and I’d like to acknowledge those who remind me so. Let’s take a peep into my world for the next 3 years.

text: Spill-over of sustainability values and practices - a psychology PhD thesis proposal The following presentation relates to my proposed PhD topic. As an audience you’re probably reading the title and wondering what relevance my topic has to the symposium theme Claiming Spaces. My immediate response is ‘nothing’. Nada, zilch, kore. As a ‘fill-in’ speaker for a presenter unable to be here, I’m reminded that despite my topics irregularity in the programme, I claim a space as both a psychologist and Maori person seeking to work with in the field of sustainability and conservation. Psychologists and Maori are interested in more than mental health and clinical investigation. We are interested in how the world goes around and seek to claim a space here too. So, this symposium and my participation DOES have relevance and I’d like to acknowledge those who remind me so. Let’s take a peep into my world for the next 3 years.

year: 2008