Mathematical Sciences: Analysis in the Large

艾萨克·查维尔和埃德加·费尔德曼将继续研究流形的微小扰动对流形的谱和随机性质的影响。这些研究已经从研究拉普拉斯的特征值与流形的几何和拓扑的关系发展到考虑这些问题的概率公式。要研究的流形的特殊扰动包括增加细长的手柄、删除子流形的管状邻域或移除小区域。研究人员还将考虑布朗运动和热扩散的大时间渐近性。

Isaac Chavel and Edgar Feldman will continue their investigations of the effect of small perturbations of a manifold on the spectral and stochastic properties of the manifold. These investigations have progressed from studying the relation of eigenvalues of the Laplacian to the geometry and topology of the manifold to consideration of probabilistic formulations of these questions. The particular perturbations of the manifolds to be studied include adding long thin handles, deleting tubular neighborhoods of submanifolds or removing small domains. The investigators will also consider large time asymptotics of Brownian motion and heat diffusion.