After the philosopher's stone : aesthetic interrogations and navigations : an exegesis presented in partial fulfilment of the requirements for the degree of Masters of Fine Arts at Massey University, Wellington, New Zealand

“One becomes two, two becomes three, and out of the third comes the One as the fourth.” Maria Prophetessai The axiom of Maria is an alchemical percept illustrating a processual procedure across time that accords with the Jungian concept of individuation (from undifferentiated unconsciousness to unique individualised wholeness). The process concerns transformations of materialities and psychological state as movement in time. My research project is situated at a nexus between three simultaneous aims and procedures which relate to this precept; One: Art as magick, (magickal operations, in this case sigil constructions, aimed at altering psychological and material conditions under intentional application of imagination and will); Two: Art as spiritual practice and religious devotion, (a devotional orientation through art practiced on a relational line of enquiry and association via ‘theophanic’ and ‘active’ imagination’); Three: Art as a psychotherapeutic vehicle (oblique means for mending disturbed subjective conditions, generating processes and affects of integration and connectivity across an experiential and theorised fragmented subject terrain). The ‘fourth’ here is what is brought to the moment of reception and reading by a given audience. All concern alchemical transmutation as matter-mind relations; from an immersive, undifferentiated ‘one’ in relative unconsciousness, to compounding relational reflexivities of correspondence, doubling of associations, ‘two’, through to a ‘third that becomes a One as the fourth’, a ‘transcendent function’, as a held space weaving all of the varying threads and development together into a new unified configuration, co-ordinated but remaining unfixed as end and determination. Each point in this axiomatic evolution is polymorphous, yet relates to origins and concerns guiding it at the outset. Drawings, objects, materialities, substances, space, become the axes and in potentia through which this metamorphic generation takes place and manifests in form

Non-embeddability of certain classes of Levi flat manifolds

On the basis of a result of Barrett, we show that members of certain classes of abstract Levi flat manifolds with boundary, whose Levi foliation contains a compact leaf with contracting, flat holonomy, admit no $CR$ embedding as a hypersurface of a complex manifold.Comment: 8 pages, no figure

The circle quantum group and the infinite root stack of a curve (with an appendix by Tatsuki Kuwagaki)

In the present paper, we give a definition of the quantum group $\mathbf{U}_\upsilon(\mathfrak{sl}(S^1))$ of the circle $S^1\colon =\mathbb{R}/\mathbb{Z}$, and its fundamental representation. Such a definition is motivated by a realization of a quantum group $\mathbf{U}_\upsilon(\mathfrak{sl}(S^1_\mathbb{Q}))$ associated to the rational circle $S^1_\mathbb{Q}\colon= \mathbb{Q}/\mathbb{Z}$ as a direct limit of $\mathbf{U}_\upsilon(\widehat{\mathfrak{sl}}(n))$'s, where the order is given by divisibility of positive integers. The quantum group $\mathbf{U}_\upsilon(\mathfrak{sl}(S^1_\mathbb{Q}))$ arises as a subalgebra of the Hall algebra of coherent sheaves on the infinite root stack $X_\infty$ over a fixed smooth projective curve $X$ defined over a finite field. Via this Hall algebra approach, we are able to realize geometrically the fundamental and the tensor representations, and a family of symmetric tensor representations, depending on the genus $g_X$, of $\mathbf{U}_\upsilon(\mathfrak{sl}(S^1_\mathbb{Q}))$. Moreover, we show that $\mathbf{U}_\upsilon(\widehat{\mathfrak{sl}}(+\infty))$ and $\mathbf{U}_\upsilon(\widehat{\mathfrak{sl}}(\infty))$ are subalgebras of $\mathbf{U}_\upsilon(\mathfrak{sl}(S^1_\mathbb{Q}))$. As proved by T. Kuwagaki in the appendix, the quantum group $\mathbf{U}_\upsilon(\mathfrak{sl}(S^1))$ naturally arises as well in the mirror dual picture, as a Hall algebra of constructible sheaves on the circle $S^1$.Comment: 63 pages, Latex; Introduction largely rewritten, a new section comparing $\mathbf{U}_\upsilon(\mathfrak{sl}(S^1_\mathbb{Q}))$ to other known infinite quantum groups is added, as well as an appendix by T. Kuwagaki giving a mirror dual construction of $\mathbf{U}_\upsilon(\mathfrak{sl}(S^1_\mathbb{Q}))$; v3: 64 pages, Final version published in Selecta Mathematic

Leakage and dephasing in 28^{28}Si-based exchange-only spin qubits

Exchange-only spin qubits hosted in $^{28}$Si-based triple quantum dots do not suffer from decoherence caused by randomly fluctuating nuclear-spin ensembles and can be relatively robust against electrical noise when operated at a sweet spot. Remaining sources of decoherence are qubit relaxation, leakage out of the qubit subspace, and dephasing due to residual effects of charge noise, the latter two of which are the focus of this work. We investigate spin-orbit-mediated leakage rates to the three-spin ground state accompanied by virtual (i) tunneling, (ii) orbital excitation, and (iii) valley excitation of an electron. We find different power-law dependencies on the applied magnetic field $B$ for the three mechanisms as well as for the two leakage rates, ranging from $\propto B^5$ to $\propto B^{11}$, and identify the sweet spot as a point of minimal leakage. We also revisit the role of electrical noise at the sweet spot, and show that it causes a decay of coherent qubit oscillations that follows a power law $\propto 1/t$ (as opposed to the more common exponential decay) and introduces a $\pi/2$ phase shift.Comment: 10 pages, three figures. Minor changes with respect to the previous version. The supplemental material is now included as appendice

The Wage-Productivity Gap Revisited: Is the Labour Share Neutral to Employment?

This paper challenges the prevailing view of the neutrality of the labour income share to labour demand, and investigates its impact on the evolution of employment. Whilst maintaining the assumption of a unitary long-run elasticity of wages with respect to productivity, we demonstrate that productivity growth affects the labour share in the long run due to frictional growth (that is, the interplay of wage dynamics and productivity growth). In the light of this result, we consider a stylised labour demand equation and show that the labour share is a driving force of employment. We substantiate our analytical exposition by providing empirical models of wage setting and employment equations for France, Germany, Italy, Japan, Spain, the UK, and the US over the 1960-2008 period. Our findings show that the time-varying labour share of these countries has significantly influenced their employment trajectories across decades. This indicates that the evolution of the labour income share (or, equivalently, the wage-productivity gap) deserves the attention of policy makers