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This dissertation is a study of the relations of Saugeen Ojibway Nation in Southwestern Ontario with British and other European settlers, the British colonial state and Canadian nation. It is committed to an illumination of the experience of Indigenous peoples as waves of migrants surrounded and enclosed them in new ways of life. The dissertation draws partially on unpublished sources, and some material culture, in particular wampum, but is principally based on published primary sources including government letters, documents, and reports; settler diaries; newspaper articles; school texts books; and Indigenous created records, testimonials, and collections of interviews. The Anishinaabe ways of living made them appear to be an obstacle to the aims of settlers, the British Crown, and later Canadian government. The sections of the dissertation examine key episodes: initial engagements between the Saugeen Ojibway Nation and early settlers (1830s-1880s), pre-confederation land treaties and the discontent they engendered (1836-1861), and the tragedy of the Residential Schools (1830s-1960s), seeking to map a the evolution of relationships between Canada and the Saugeen Ojibway Nation as Canada increasingly sought to remove Indigenous peoples by way of either assimilation or extermination. But there was also, from the outset, an alternative experience of peaceful and respectful coexistence, and the dissertation attempts, in all these sections, to make this visible. Today, the population within Canadian borders is comprised of sovereign Indigenous peoples, the descendants of settlers, and newcomers. The thesis is intended to be a contribution to a new history of Canada as a shared space.

We study correlated two-level quantum impurity models coupled to a metallic conduction band in the hope of gaining insight into the physics of nanoscale quantum dot systems. We focus on the possibility of formation of a spin-1 impurity local moment which, on coupling to the band, generates an underscreened (USC) singular Fermi liquid state. By employing physical arguments and the numerical renormalization group (NRG) technique, we analyse such systems in detail examining in particular both the thermodynamic and dynamic properties, including the differential conductance. The quantum phase transitions occurring between the USC phase and a more ordinary Fermi liquid (FL) phase are analysed in detail. They are generically found to be of Kosterlitz-Thouless type; exceptions occur along lines of high symmetry where first-order transitions are found. A `Friedel-Luttinger sum rule' is derived and, together with a generalization of Luttinger's theorem to the USC phase, is used to obtain general results for the $T=0$ zero-bias conductance --- it is expressed solely in terms of the number of electrons present on the impurity and applicable in both the USC and FL phases. Relatedly, dynamical signatures of the quantum phase transition show two broad classes of behaviour corresponding to the collapse of either a resonance or antiresonance in the single-particle density of states. Evidence of both of these behaviours is seen in experimental devices. We study also the effect of a local magnetic field on both single- and two-level quantum impurities. In the former case we attempt to resolve some points of contention that remain in the literature. Specifically we show that the position of the maximum in the spin resolved density of states (and related peaks in the differential conductance) is not linear in the applied field, showing a more complicated form than a simple `Zeeman splitting'. The analytic result for the low-field asymptote is recovered. For two-level impurities we illustrate the manner in which the USC state is destroyed: due to two cancelling effects an abrupt change in the zero-bias conductance does not occur as one might expect. Comparison with experiment is made in both cases and used to interpret experimental findings in a manner contrary to previous suggestions. We find that experiments are very rarely in the limit of strong impurity-host coupling. Further, features in the differential conductance as a function of bias voltage should not be simply interpreted in terms of isolated quantum dot states. The many-body nature of such systems is crucially important to their observed properties.