Special Analysis Seminar: An introduction to the bulk-edge correspondence

Seminar | February 20 | 4:10-5 p.m. | 736 Evans Hall

 Alexis Drouot, Columbia University

 Department of Mathematics

Physical experiments show that interfaces between dissimilar media act as stable channels for the propagation of energy. In discrete models, this stability is explained via an index-like theorem: the bulk edge correspondence. I will first review this principle, which connects the effective number of waves propagating along the interface (a spectral invariant) to a Chern number (a topological invariant).

I will then focus on a PDE modeling conduction in a graphene layer with a line defect. In a perturbative regime, Fefferman–Lee-Thorp–Weinstein–Zhu constructed waves propagating along the defect. I will show that precisely two of them are topologically stable: they persist outside the perturbative regime. I will then calculate the associated Chern number: it is 2 or -2. These results illustrate the bulk-edge correspondence in a continuous setting.