Mathematical Sciences: Geometry of Classical Banach Spaces and Convex Bodies

Alspach将研究绝对可和序列空间的前公演及其与连续函数空间的关系。特别地，要考虑诸如这些前公数中哪些是具有可分离对偶的连续函数空间的商之类的问题。Schutt将继续研究凸体的浮体，并将研究扩展到随机多面体及其与多面体逼近和超平面问题的关系。巴拿赫空间理论是数学的一部分，它试图将三维欧几里得空间（即普通空间）的结构推广到无限多维。巴拿赫空间中距离函数的公理比欧几里得距离的公理更宽松（例如，“平行四边形定律”不需要成立），因此，巴拿赫空间的“几何”可能相当奇特。该领域的研究主要集中在Banach空间的结构理论研究上。

Alspach will investigate the preduals of the space of absolutely summable sequences and their relation to the spaces of continuous functions. In particular, questions such as which of these preduals are quotients of a space of continuous functions with separable dual are to be considered. Schutt will continue his investigation of the floating body of a convex body and extend the investigations to random polytopes and their relation to polyhedral approximation and the hyperplane problem. Banach space theory is that part of mathematics that attempts to generalize to infinitely many dimensions the structure of 3-dimensional Euclidean (i.e.ordinary) space. The axioms for the distance function in a Banach space are more relaxed than those for Euclidean distance (For example, the "parallelogram law" is not required to hold.), and as a result, the "geometry" of a Banach space can be quite exotic. Much of the research in this area concerns studying the structure theory of Banach spaces.