van Winter Memorial Lecture in Mathematical Physics

  • Academic Administration Associate, Department of Mathematics
  • Mathematics
731 Patterson Office Tower
(859) 257-6808
Date: 
03/29/2017 - 4:00pm to 5:00pm
Location: 
155 Chemistry-Physics Building
Speaker(s) / Presenter(s): 
Professor Michael Weinstein

Abstract: In many applications, e.g. photonic and quantum systems, one is interested in controlled localization of wave energy.

Edge States are a type of localization along a line-defect or interface between media. We study edge states in honeycomb structures (such as graphene and its photonic analogues) and discuss their novel properties. In particular, we examine the formation of Topologically Protected Edge States, which persist and are stable against strong local distortions of the edge, and are therefore potential vehicles for robust energy-transfer in the presence of defects and random imperfections.

We further discuss rigorous results and conjectures for families of continuum PDE models (Schroedinger and Maxwell) admitting edge states which are topologically protected, edge states which are not protected, and states which remain localized near an edge for a very long time, but likely decay eventually.

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