Compactifications and Local-to-Global Structure for Bruhat-Tits Buildings

我们计划研究Bruhat-Tits建筑的紧凑化和局部-全局原理。紧凑化将被构建为双函数完成，从建筑最大单位上的不对称多面体规范开始。其最终目标是研究建筑物上离散群体作用的动力学。我们的方法使用超积、拓扑向量空间和CAT(0)几何，基于局部-全局原理，我们计划研究Bruhat-Tits建筑的室图中的度量球。最近对一类特殊的Bruhat-Tits建筑的结果表明，函数域和p-ady域之间存在有趣的二分法，我们想要从几何的观点来探讨这一点。

We plan to study compactifications and local-global principles of Bruhat-Tits buildings. The compactifications will be constructed as horofunction completions, starting with asymmetric polyhedral norms on the maximal flats of the building. The ultimate goal is to study the dynamics of discrete group actions on the buildings. Our methods use ultraproducts, topolgical vector spaces and CAT(0) geometry.For the local-global principles we plan to study metric balls in the Chamber graphs of Bruhat-Tits buildings. Recent results for a special class of Bruhat-Tits buildings indicate that there is an interesting dichotomy between the case of function fields and p-adic fields, which we want to explore from a geometric viewpoint.