Geometrical Methods, non Self-Adjoint Spectral Problems, and Stability of Periodic Structures (17w5044)


(University of Michigan)

(University of Illinois at Urbana-Champaign)

Ramón Plaza (Universidad Nacional Autónoma de México)


The Casa Matemática Oaxaca (CMO) will host the "Geometrical Methods, non Self-Adjoint Spectral Problems, and Stability of Periodic Structures" workshop from June 18th to June 23rd, 2017.

In the physical world there are many instances of coherent structures, including the Great Red Spot on Jupiter, a tsunami wave propagating across the ocean, or a pulse of light propagating through an optical fiber. The idea that unifies these disparate phenomena is that of stability. Structures which are stable are robust: they form easily, without regard to small details of the problem, and persist for long times. For these reasons coherent structures are important for understanding the behaviour of the underlying system. At the theoretical level the question of stability reduces to understanding an eigenvalue problem, a mathematical construct that helps to quantify this robustness. One key idea is that in many cases geometrical information (such as the ``shape'' of the wave) can be parleyed into powerful tools of analysis for studying stability.

In this workshop we bring together researchers working on questions of stability in many different contexts and using many different methodologies, including geometrical, analytical and numerical approaches. We believe that this will provide a fertile ground for interaction between researchers in many different subfields, and will lead to new approaches and new understanding for many different physical systems. Moreover, the workshop also aims to foster global collaborative efforts to address these scientific challenges, and to develop initiatives involving graduate students and scientists at all levels of experience. The workshop will enhance the research environment in the host country of the meeting and abroad.

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.