Emil Prodan | Topological Bulk-Boundary Correspondence via K-Theory

Speaker: Emil Prodan, Yeshiva

Title: Topological Bulk-Boundary Correspondence via K-Theory

Abstract: I will demonstrate how K-Theory becomes one of the finest tools available when it comes to establishing the bulk-boundary correspondence in aperiodic systems. For example, the closely related quasi-periodic and quasi-crystalline systems display the same bulk K-theory but they have a completely opposite edge physics: topological edge spectrum exists for the first class of systems but it is entirely absent for the second class. The K-Theory of the edge and its relation with the bulk explain the differences. I will then demonstrate how the K-Theoretic guidance lead to concrete engineering of many aperiodic meta-materials where topological pumping is possible.