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The K-theoretic Bulk-Boundary Principle for Patterned Resonators

Banff International Research Station for Mathematical Innovation and Discovery

Resonators couple to each other when put in contact, leading to collective resonant modes. An interesting problem is to understand and exploit these collective modes when the resonators form different patterns in space. In this talk I will first present a kaleidoscope of numerical examples where patterned resonators display spectral properties akin to 2- and higher-dimensional Integer Quantum Hall Effect. In the second part, I will demonstrate how K-theory can be used to understand and predict the bulk and the edge spectrum of such systems. In particular, a simple K-theoretic version of the bulk-boundary principle will be presented which enables one to see when topological edge spectrum is to be expected. This last part will be supported again with a kaleidoscope of numerical examples.

Mathematics; Partial differential equations; General topology

video/mp4

Author affiliation: Yeshiva University

2018-04-07

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/65164

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/