Towards logarithmic representation theory of W-algebras

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Aims: To construct and analyse indecomposable representations of significance in conformal field theory. Significance: Conformal field theory plays a key role in many developments in mathematics and physics. Logarithmic conformal field theories govern important systems such as two-dimensional critical percolation. This proposal aims to develop the representation theory necessary for understanding salient features of critical systems described by logarithmic conformal field theory. Expected Outcomes: Novel representations of fundamental importance in logarithmic conformal field theory. Benefit: Resolution of open problems in logarithmic conformal field theory, thus continuing the strong tradition in the field in Australia.