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

Mauldin计划研究圆和其他物体的同胚的随机生成。计算机研究在这里很有用。他计划进一步发展计算和估计豪斯多夫维数和测量的方法，特别是在动力系统和随机几何指令的背景下。这包括对weerstrass无处可微函数的分析。他计划描述那些在某些度规上具有有限线性测度的连续体。他计划在描述集理论中进一步发展应用于正交转移核（正算子）和1-1选择的技术。

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.