粗几何及其在固态物理中的应用

Coarse geometry and topological phases

We propose the Roe C*-algebra from coarse geometry as a model for topological phases of disordered materials. We explain the robustness of this C*-algebra and formulate the bulk-edge correspondence in this framework. We describe the map from the K-theory of the group C*-algebra of Z^d to the K-theory of the Roe C*-algebra, both for real and complex K-theory.

Gaplessness of Landau Hamiltonians on hyperbolic half-planes via coarse geometry

We use coarse index methods to prove that the Landau Hamiltonian on the hyperbolic half-plane, and even on much more general imperfect half-spaces, has no spectral gaps. Thus the edge states of hyperbolic quantum Hall Hamiltonians completely fill up the gaps between Landau levels, just like those of the Euclidean counterpart.

自旋系统的普适粗几何

Universal coarse geometry of spin systems

本文为自旋系统的态和动力学定义了普适粗几何结构，证明其在准局域扰动下稳定，并建立了序参量与量子电路动力学粗结构之间的相容性。

电导的量子化与划分的粗上同调

Quantization of conductance and the coarse cohomology of partitions

本文证明霍尔电导的整数量子化源于样品的大尺度几何，通过将费米投影与划分导出的粗上同调类进行高阶迹配对并证明其整性。

软非晶固体中应力的耗散异常：密度奇异性的足迹

Dissipative anomalies of stresses in soft amorphous solids: footprints of density singularities

本文基于Onsager理想湍流理论框架，研究软非晶固体零温下塑性应力耗散的结构起源，证明密度奇异性可引发应力降，揭示无热无序系统流动对应低Besov正则性的粗粒度NDE方程紫外不动点解。