A noncommutative framework for topological insulators

We study topological insulators, regarded as physical systems giving rise to topological invariants determined by symmetries both linear and anti-linear. Our perspective is that of noncommutative index theory of operator algebras. In particular we formulate the index problems using Kasparov theory, both complex and real. We show that the periodic table of topological insulators and superconductors can be realised as a real or complex index pairing of a Kasparov module capturing internal symmetries of the Hamiltonian with a spectral triple encoding the geometry of the sample's (possibly noncommutative) Brillouin zone.Comment: 32 pages, final versio

Contrasting the use of space in post-Roman Exeter:geoarchaeology of dark earth and medieval deposits below Exeter Cathedral

European urban dark earth investigations have aided our understanding of Late Roman and early medieval populations and their activities. Deposits from two locations below Exeter Cathedral were compared in a geoarchaeological study and contrasting uses of space were identified. This supports the need for case-by-case investigations of urban deposits

A preliminary assessment of water partitioning and ecohydrological coupling in northern headwaters using stable isotopes and conceptual runoff models

Funded by European Research Council ERC. Grant Number: GA 335910 VEWA Swedish Science Foundation (SITES) Future Forest Formas (ForWater) SKB the Kempe foundation Environment Canada the Garfield Weston Foundation the Natural Sciences and Engineering Research Council of Canada (NSERC) the Northwest Territories Cumulative Impacts Monitoring ProgramPeer reviewedPublisher PD

The KO-valued spectral flow for skew-adjoint Fredholm operators

In this article we give a comprehensive treatment of a `Clifford module flow' along paths in the skew-adjoint Fredholm operators on a real Hilbert space that takes values in KO${}_{*}(\mathbb{R})$ via the Clifford index of Atiyah-Bott-Shapiro. We develop its properties for both bounded and unbounded skew-adjoint operators including an axiomatic characterization. Our constructions and approach are motivated by the principle that $$\text{spectral flow} = \text{Fredholm index}.$$ That is, we show how the KO--valued spectral flow relates to a KO-valued index by proving a Robbin-Salamon type result. The Kasparov product is also used to establish a spectral flow $=$ Fredholm index result at the level of bivariant K-theory. We explain how our results incorporate previous applications of $\mathbb{Z}/ 2\mathbb{Z}$-valued spectral flow in the study of topological phases of matter.Comment: v2: 47 pages, applications to physics expande

New methods for investigating slag heaps: Integrating geoprospection, excavation and quantitative methods at Meroe, Sudan

This paper describes a multifaceted approach to the investigation of iron slag heaps, focusing on one of the slag heaps at the Royal City of Meroe in Sudan. This study marries together geoprospection data (gradiometry and electrical resistivity transects), topographic data and quantitative excavation data, to provide an analysis and comparison of the total volume, slag component and slag composition of a slag-heap. Significantly, the results demonstrate the limitations of using a topographic only model, but also demonstrate how volumetric modelling must be integrated within quantitative characterisation of slag-heap composition. In this case, quantitative sampling of the slag deposits revealed the composition of the slag assemblage was dominated by a newly defined category of slag which has major implications for reconstructing iron technologies in the Meroitic civilisation. This research highlights the dangers of applying simplistic models and basic investigative strategies to iron slag heaps and furthers the debate on applying volumetric modelling and excavation sampling to unexcavated areas of the finite and important resource of archaeometallurgical deposit sequences.Qatar Sudan Archaeology Project grant 037 UCL Qatar core fundin