On the p-Laplace operator on Riemannian manifolds

This thesis covers different aspects of the p-Laplace operators on Riemannian manifolds. Chapter 2. Potential theoretic aspects: the Khasmkinskii condition. Chapter 3: sharp eigenvalue estimates with Ricci curvature lower bounds. Chapter 4: Critical sets of (2-)harmonic functions.Comment: PhD Thesis: Contains results obtained in collaboration with other mathematicians, see section 1.4 for details. ADDED IN THIS VERSION: correction of few typos, and added a reference brought to our attention by an anonymous referee. Details in the introduction, end of section 1.

Does the number sense represent number?

On a now orthodox view, humans and many other animals are endowed with a “number sense”, or approximate number system (ANS), that represents number. Recently, this orthodox view has been subject to numerous critiques, with critics maintaining either that numerical content is absent altogether, or else that some primitive analog of number (‘numerosity’) is represented as opposed to number itself. We distinguish three arguments for these claims – the arguments from congruency, confounds, and imprecision – and show that none succeed. We then highlight positive reasons for thinking that the ANS genuinely represents numbers. The upshot is that proponents of the orthodox view should not feel troubled by recent critiques of their position

Fear and loathing on the sport field: Masculinities, social transformation and creative teaching strategies

The apparent links between sport and masculinities has generated critical concern from a number of educationalists, feminists and sport sociologists. These concerns have inspired the development of various pedagogical strategies for transforming understandings and practices of gender within educational settings. This paper reviews the connections between sport and masculinities, and contributes to the development of a critical pedagogy by illustrating how the creative arts can be used within tertiary educational settings to raise awareness of the gendering influence of sport. I detail how I drew on Foucauldian theorizing and the work of Laurel Richardson to develop a teaching strategy, involving the use of dance and a 'collective story', to promote marginalised knowledge and stir political emotions. I present a shortened version of the collective story and discuss its impact on tertiary students. I conclude by encouraging other educators to draw on the creative arts as tools for promoting discussion, legitmating the voice of the 'other' and to encourage an empathetic response