We study one dimensional insulators obeying a chiral symmetry in the single-particle picture where the Fermi energy is assumed to lie within a mobility gap. Topological invariants are defined for infinite (bulk) or half-infinite (edge) systems, and it is shown that for a given bulk system with nearest neighbor hopping, the invariant is equal to the induced-edge-system's invariant. We also give a new formulation of the topological invariant in terms of the Lyapunov exponents of the system, which sheds light on the conditions for topological phase transition extending to the mobility gap...

# Mathematical Physics Seminar

Organizer(s):

For more information about this seminar, contact Michael Aizenman

**Please click on seminar title for complete abstract.**

November 28, 2017

4:30pm - 5:30pm

##### TBA - Dr. Efi Efrati

Location

Jadwin Hall 343

Speaker: Dr. Efi Efrati,

Weizmann Institute

Weizmann Institute

December 5, 2017

4:30pm - 5:30pm

##### Bulk-Edge Duality and Complete Localization for Chiral Chains

Location

Jadwin Hall 343

Speaker: Jacob Shapiro,

ETH

ETH