Almost-Periodic Spectral Problems (22w5163)


David Damanik (Rice University)

Svetlana Jitomirskaya (UC Berkeley)

Leonid Parnovski (University College London)


The Banff International Research Station will host the "Almost-Periodic Spectral Problems" workshop in Banff from April 17 to April 22, 2022.

Almost periodic problems have arisen in physics long ago in the study of electrons on a two-dimensional lattice exposed to a constant magnetic field with irrational flux (the Harper model), and more recently (in the 1980's) in the study of electrons in quasi-crystals (the Fibonacci model). It has turned out that, unlike periodic problems where one has a powerful tool for their study (Floquet-Bloch decomposition), almost periodic operators are very difficult to study, and the earliest mathematical results on these operators were obtained in the late 1970's. Since then many people have devoted their efforts to the study of spectral properties of almost periodic problems, including Avila, Bourgain, Sarnak, Simon, and Sinai. The spectral theory of almost periodic operators is much richer than that of periodic operators, with new phenomena such as Cantor spectra, purely singular continuous spectral measures or Anderson-type localization occurring in a natural, and in some settings generic, way.

Given the progress that has been made recently and the multitude of tools that have been employed, the meeting brings together people with various backgrounds to present recent results, exchange ideas, learn new methods, and potentially start new collaborations.

Junior participants (including current PhD students who may have been exposed to only one perspective and set of tools so far) will have the opportunity to experience the breadth of the area and the whole arsenal of technical tools that have been used successfully in recent advances.

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).