Topics in random matrix theory and spectral theory of operators on Riemannian manifolds.

大系统是复杂系统的有效代表，它是由许多服从简单二元相互作用规则的基本组分组成的。随着成员数量的增加，涉及大量基本要素的集体行为出现了.事实证明，大型随机矩阵的特征值--借助掷骰子绘制的数字方阵（这说明了随机性）及其涉及微分的连续推广--也以类似的方式表现。在这些项目中，特征值在这两种情况下的行为将为模型复杂系统提供价值见解。

Large systems consisting of many elementary components obeying simple binary interaction rule are very effectiverepresentatives of complex systems. As the number of constituents increases collective behaviour involving largenumber of the elementaries emerges. It turns out that eigenvalues of large random matrices --- square array of numbers drawn with theaid of the throw of a die (which accounts for the randomness) and itscontinuous generalization involving differentiation---also behave in a similar manner. In these projects the behaviour of thethe eigenvalues in both instances will give value insights into the model complex systems.