Non-Hermitian topology and exceptional-point geometries

Non-Hermitian theory is a theoretical framework used to describe open systems. It offers powerful tool in the characterization of both intrinsic degrees freedom system and interactions with external environment. The non-Hermitian consists mathematical structures that are fundamentally different from those Hermitian theories. These not only underpin novel approaches for precisely tailoring systems applications but also give rise topologies found In this Review, we provide an overview topology by establishing its relationship behaviours complex eigenvalues biorthogonal eigenvectors. Special attention given exceptional points — branch-point singularities on eigenvalue manifolds exhibit nontrivial topological properties. We discuss recent developments band topology, such as skin effect classifications. systems, which can This Review provides discusses developments,