Title: Topological Applications of p-Adic Divergence and Gradient Operators Show Chinese title

Title: p进散度和梯度算子的拓扑应用

Abstract: $p$-Adic divergence and gradient operators are constructed giving rise to $p$-adic vertex Laplacian operators used by Z\'u\~niga in order to study Turing patterns on graphs, as well as their edge Laplacian counterparts. It is shown that the Euler characteristic of a finite graph can be expressed via traces of certain heat kernels associated with these new operators. This result is applied to the extraction of topological information from Mumford curves via heat kernels. Show Chinese abstract

Abstract: $p$-Adic散度和梯度算子被构造出来，产生了$p$-Adic顶点拉普拉斯算子，Zúñiga利用这些算子来研究图上的Turing模式，以及它们的边拉普拉斯算子对应物。 展示了有限图的欧拉特征可以通过与这些新算子相关的某些热核的迹来表示。 该结果被应用于通过热核从Mumford曲线中提取拓扑信息。