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.
Corrine Elliott was awarded a 2016 Goldwater Scholarship. The Barry Goldwater Scholarship and Excellence in Education Program was established by Congress in 1986 to honor Senator Barry Goldwater, who served his country for 56 years as a soldier and statesman, including 30 years of service in the U.S. Senate.
The University of Kentucky Department of STEM Education, under the direction of Molly Fisher (PI), associate professor and director of graduate studies, and Jennifer Wilhelm (co-PI), professor and chair,
Computer science and the St. Chad Gospels. Physics and Spanish. Math and international studies. The combination of these don't seem to make a lot of sense, but it is these interests that have shaped the undergraduate career of one UK senior.
Adib Bagh, assistant professor in the departments of mathematics and economics at the University of Kentucky, was recently quoted in a March 16 Wall Street Journal article examining office bracket pools for the NCAA men's basketball tournament.