Localization of Eigenfunctions of Elliptic Operators (15frg188)


(Universite Paris XI, France)

(Ecole Polytechnique; France)

David Jerison (Massachusetts Institute of Technology)

(University of Minnesota)


The Banff International Research Station will host the "Localization of Eigenfunctions of Elliptic Operators" workshop in Banff from March 27 to April 4.

Wave localization is an astonishing ability of physical systems to maintain standing waves in a small portion of the original domain, preventing extended propagation. It is ubiquitous in nature and in man-made mechanisms: mechanical vibrations, sound, light, and even matter in quantum physics are systematically affected by extremely powerful or highly detrimental localization effects. Nonetheless, its intricate nature, exact triggers, frequencies, and perplexing rules of confinement remain largely a mystery. The goal of the present project is to reveal mathematical mechanisms governing wave localization, to be able to predict location and frequencies of the confined vibrations, and to establish mathematical tools which would enable scientists and engineers to design the systems with the desired localization properties.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).