## Mathematical and Physical Aspects of Topologically Protected States

### K -theory via the emergent topology of insulators

Terry Loring

University of New Mexico
[SLIDES]

Abstract:

This talk will begin with an elementary discussion of approximately compatible observables and issues of simultaneous measurement. Working on finite dimensional Hilbert space, this discussion leads to invariants based on very elementary K-theory. The remainder of the talk will discuss joint work with Hermann Schulz-Baldes, proving in some generality the equality of these finite-volume K-theory invariants with established invariants in infinite volume insulators. These finite-volume invariants can be defined on models with irregular boundaries, lattice defects, and can work with sites in real space that are random or quasicrystalline. Simple formulas for these finite-volume invariants allow for fast numerics and quantitative statements about the robustness of certain states against disorder.