Coherent Structures in PDEs and Their Applications (16w5050)


Theodore Kolokolnikov (Dalhousie University)

(University of California Los Angeles)

(San Diego State University)

Panos Kevrekidis (University of Massachusetts Amherst)

Paul Newton (University of Southern California)

(University of San Francisco)


The Casa Matemática Oaxaca (CMO) will host the "Coherent Structures in PDEs and and Their Applications." workshop from June 19th to June 24th, 2016.

In 1920's Einsein and Bose proposed a new state of matter, now called Bose-Einsein Condensates (BEC), which can exist at extremely low temperatures (close to absolute zero), and which consists of concentrations of atoms. It was not until 1990's that their existence was experimentally observed at JILA and MIT, a work for which these groups were awarded the Nobel prize in Physics (2001). In these experiments, rubidium or sodium atoms were observed to form coherent localized waveforms. Subsequently, coherent structures such as solitary waves, vortices or vortex rings were produced experimentally and a considerable amount of theoretical studies was focused on their mathematical and computational understanding.

Recent studies of the these systems have identified vibrational modes of multiple dark solitary waves in 1D and explored the bifurcations and formation of a crystalline lattice structures (and its own vibrational -so-called Tkachenko- modes) for vortices in 2D in close coordination with state-of-the-art experimental results. The interactions of such localized states can be reduced to effective particle systems. The purpose of this workshop is to further the understanding of these and related localized structures.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide 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 in Banff 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). The research station in Oaxaca is funded by CONACYT.