报告题目： Sphere uniform homeomorphism of Banach spaces and its applications

报告摘要：Let E and F be two Banach spaces. We say that their unit spheres S(E) and S(F) are uniformly homeomorphic if there is a bijection f from S(E)  onto S(F) such that f and its inverse f^{-1} are uniformly continuous. In this talk, we will focus on those Banach spaces whose unit spheres are uniformly homeomorphic  to the unit sphere of Hilbert space. As a result, applying the finite dimensional pieces approach, we give the (sharp) quantitative versions of several known results concerning sphere uniform homeomorphisms in the literature. Some related applications, involved the coarse embeddings of expander graphs, Kasparov-Yu's property (H) and the approximation nearest neighbors search (the ANN problem) in computer science field,  will be introduced and considered.

主讲人：程庆进

报告时间：2019年12月13日 15:30

报告地点：精工楼7-103

个人简介：程庆进，厦门大学数学科学学院，教授，博士生导师。主要研究方向是Banach空间非线性几何及其应用。（与程立新教授合作）提出并研究了Banach空间中的超弱紧集理论；解决了非线性谱系不等式关于指数p的稳定性问题。先后承担国家基金委重点项目、国家基金委面上项目、国家基金委青年项目和教育部新教师项目等。在J. Convex Anal、J Funct Anal、Studia Math、Sci. China Ser. A等国际期刊上发表SCI学术论文20多篇。