System of Hodge Bundles and Generalized Opers on Smooth Projective Varieties

Let $k$ be an algebraically closed field of any characteristic. Let $X$ be a polarized irreducible smooth projective algebraic variety over $k$. We give criterion for semistability and stability of system of Hodge bundles on $X$. We define notion of generalized opers on $X$, and prove semistability of the Higgs bundle associated to generalized opers. We also show that existence of partial oper structure on a vector bundle $E$ together with a connection $\nabla$ over $X$ implies semistability of the pair $(E, \nabla)$.Comment: Typos corrected, acknowledgement added. To appear in the Journal of Geometry and Physic

Homecomings: genealogy, heritage-tourism & identity in the Scottish Highland diaspora

This work is concerned with the processes through which members of diasporic communities, construct and negotiate aspects of their identities in relation to perceived ancestral homelands. Addressing a central paradox of globalization-the contrary movement towards localization-I examine the role of place, belonging and territorial attachment in an age often characterized by placelessness, mobility and deterritorialization. More particularly, the thesis explores flows of people, images, objects, ideas, symbols and stories within a posited Scottish diaspora, focusing on journeys made by people who claim Scottish Highland descent ordinarily living in the USA, Canada, Australia, New Zealand, and other regions in which Scottish migrants have historically settled, to the Scottish Highlands and Islands, pursuing genealogical research and seeking out places associated with their ancestors. Many such travellers define their journeys, contra tourism, as homecomings, quests and pilgrimages: I interrogate these assertions, considering in what ways these secular practices may be regarded as sacred acts. Through the agency of these genealogical 'journeys of discovery', I suggest that individuals are able to construct meaningful, morally-defensible and 'authentic' self-narratives from the ambiguities and discontinuities of their migrant histories, thus recovering a sense of being 'at home' in the 'maelstrom' of modernity. It is ironic that such localizing strategies are often enabled through globalizing technologies such as the internet, and, indeed, it is through the global mediascape that the Highland homeland is 'imagineered' in diasporan consciousness. I consider the relationship between these discursive realms and the material realms of the homeland, arguing that, whilst the two are inseparable, it is ultimately the phenomenological encounter with the material landscape of the Scottish Highlands and Islands that confers substance to the heritage-tourists' identity claims. The research is based on fieldwork conducted throughout the Scottish Highlands and Islands and among online Scottish heritage communities between 1998 and 2001

Consistent 3D Quantum Gravity on Lens Spaces

We study non-perturbative quantization of 3d gravity with positive cosmological constant (de Sitter space being the prototype vacuum solution, whose Euclideanization of course gives the three sphere) on the background topology of lens space, which is a three spheres modulo a discrete group. Instead of the strategy followed by a recent work \cite{Castro:2011xb}, which compares results in the second and first order formulations of gravity, we concentrate on the later solely. We note, as a striking feature, that the quantization, that relies heavily on the axiomatics of topological quantum field theory (TQFT) can only be consistently carried by augmenting the conventional theory by an additional topological term coupled through a dimensionless parameter. More importantly the introduction of this additional parameter renders the theory finite.Comment: New section and references added. Accepted in Phys. Rev. D for publicatio

The clarity incentive for issue engagement in campaigns

Although parties focus disproportionately on favorable issues in their election campaigns, it is also the case that parties spend much of the ‘short campaign’ addressing the same issues – and especially salient issues. If able to influence the importance of issues for voters through their emphasis, it is puzzling that parties spend any time on unfavourable issue positions. We suggest that while parties prefer to emphasize popular issue positions, they also face an additional incentive to emphasize issues that are salient to voters: clarifying their positions on these issues for sympathetic voters. Leveraging the surprise general election victory of the British Conservative party in 2015—which brought about a hitherto unexpected referendum on EU membership—we show that, consistent with this hypothesis, voter uncertainty is especially costly for parties on salient issues. We formalize this argument using a model of party strategy with endogenous issue salience.Othe

2+1 Quantum Gravity with Barbero-Immirzi like parameter on Toric Spatial Foliation

We consider gravity in 2+1 space-time dimensions, with negative cosmological constant and a `Barbero-Immirzi' (B-I) like parameter, when the space-time topology is of the form T^2 \times \mathbbm{R}. The phase space structure, both in covariant and canonical framework is analyzed. Full quantization of the theory in the 'constrain first' approach reveals a finite dimensional physical Hilbert space. An explicit construction of wave functions is presented. The dimension of the Hilbert space is found to depend on the `Barbero-Immirzi' like parameter in an interesting fashion. Comparative study of this parameter in light of some of the recent findings in literarure for similar theories is presented.Comment: Latex, Substantial changes: new sections added. Accepted for publication in Class. Quant. Garv

Entanglement Negativity in TTˉ\text{T}\bar{\text{T}}-deformed CFT2_2s

We study the entanglement negativity for various bipartite mixed states in $\text{T}\bar{\text{T}}$-deformed CFT$_2$s at a finite temperature. Utilizing the replica method, we construct a general formula for the entanglement negativity of bipartite mixed states up to first order in the deformation parameter. Subsequently, we compute the entanglement negativity for bipartite states involving two disjoint, two adjacent and a single interval utilizing our formula. Furthermore, we advance a holographic construction to compute the entanglement negativity in such bipartite states in the $\text{T}\bar{\text{T}}$-deformed CFT$_2$s and find agreement with the corresponding field theoretic results in the limit of small deformation parameter.Comment: 12 pages + 1 appendix, 5 figure