Dionne Brand, Austin Clarke, and Tessa McWatt: Blackening Canada

This project analyzes contemporary black diasporic writing in Canada, arguing that Dionne Brand, Austin Clarke and Tessa McWatt evince a unique form of double-consciousness in their writings. Their work transforms African-American double-consciousness by locating it simultaneously within both the black diaspora and the practice of Canadian multiculturalism. The objective of this project is to offer a critical framework for situating these writers within the legacy of both Black Atlantic and Canadian cultural production. These writers do not aim to resolve their double-consciousness but rather dwell within that contradictory doubleness and hyphenation, forcing nation and diaspora to contend with one another in a discomfiting and unsettling dialogue. These authors employ the absences of the black diaspora to imagine new forms of black cultural production, multicultural citizenship and national identity. Their works produce a grammar of diasporic double-consciousness that locates the absented origins of diaspora within Canada. Brand’s depiction of temporality and Clarke’s tracing of movement explore the continuities between nation and diaspora while re-membering neglected aspects of the history of black Canada, such as the life and death of Albert Johnson. McWatt extends this blackening of nation by depicting coalitions between diasporic, indigenous, raced and sexed subjects. These authors transform hegemonic Canadian narratives of nation by dwelling in the hyphen, while their evocation of memory, absence, trauma, and desire gives blackness new meaning and legitimacy.

Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.

Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation

We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion through boundary vibrations. We study the Dirichlet to Neumann operator when vibrations are imposed and data recorded on disjoint sets, a useful setting for applications. We prove that this operator determines the Dirichlet to Neumann operator where sources and observations are on the same set, provided a spectral condition on the Laplace-Beltrami operator for the manifold is satisfied. We prove this by providing an implementable procedure for determining a portion of the Riemannian manifold near the area where sources are applied. Drawing on established results, an immediate corollary is that a compact Riemannian manifold can be reconstructed from the Dirichlet to Neumann operator where sources and observations are on disjoint sets.