Mathematics of disordered topological matter

拓扑不变量及其指标理论、体边界对应（BBC）和最近引入的谱定位器是无序拓扑绝缘体的成熟数学概念，对这类材料的数值研究也有影响。本提案是关于将先前的结果和技术扩展到具有晶体缺陷，无序半金属和拓扑金属的系统，以及由（泄漏和驱动）光子学和超材料产生的非厄米拓扑系统。该建议的另一部分旨在更深入地理解这种拓扑系统上的散射。

Topological invariants and their index theory, the bulk-boundary correspondence (BBC) and the more recently introduced spectral localizer are well-established mathematical concepts for disordered topological insulators and are also influential for numerical studies of such materials. This proposal is about extending prior results and techniques to systems with crystalline defects, disordered semimetals and topological metals, as well as non-hermitian topological systems stemming from (leaky and driven) photonics and metamaterials. Another part of the proposal aims at a deeper understanding of scattering on such topological systems.