Mathematical Sciences: Geometry of Classical Banach Spaces and Convex Bodies

Alspach将研究绝对可和序列空间的乘积及其与连续函数空间的关系。特别地，要考虑这样的问题，例如这些前件中的哪些是具有可分对偶的连续函数空间的商。舒特将继续他对凸体浮体的研究，并将研究扩展到随机多面体及其与多面体近似和超平面问题的关系。Banach空间理论是试图将三维欧几里得(即普通)空间的结构推广到无限多维的数学部分。Banach空间中距离函数的公理比欧几里德距离的公理要宽松得多(例如，不需要遵守“平行四边形定律”)，因此，Banach空间的“几何”可能是相当奇异的。这方面的许多研究都涉及到对Banach空间的结构理论的研究。

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.