Mathematical Sciences: Descriptive Set Theoretic and Probabilistic Methods in Topology and Analysis

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Mauldin plans to investigate the random generation of homeomorphisms of the circle and other objects. Computer studies are useful here. He plans to develop further methods of calculating and estimating Hausdorff dimension and measure, particularly within the context of dynamical systems and random geometric instructions. This includes an analysis of the Weierstrass nowhere differentiable functions. He plans to characterize those continua which have sigma-finite linear measure in some metric. He plans to develop further techniques in descriptive set theory with applications to orthogonal transition kernels (positive operators) and 1-1 selections in mind.