# The Mathematics of Layers and Interfaces (15w5065)

## Organizers

(University of British Columbia)

Nicholas Brummell (University of California at Santa Cruz)

(University of Cambridge)

(University of California at Santa Cruz)

(University of Alberta)

## Description

The Casa Matemática Oaxaca (CMO) will host the "The Mathematics of Layers and Interfaces" workshop from November 8th to November 13th, 2015.

This workshop on the Mathematics of Layers and Interfaces" will gather together scientists from various walks of mathematical and physical sciences to explore the reasons why some fluids, despite being turbulent, show a natural tendency to form layers. These layers are well-mixed, and separated by interfaces across which fluid motions are strongly inhibited. This occurs for instance in the tropical and arctic ocean, where temperature and salinity do not vary smoothly with depth but instead have a staircase" profile. Thermohaline staircases play a potentially important role in controlling the global oceanic circulation. A similar process occurs in volcanic lakes, and regulates the release of toxic gases into the atmosphere. Interestingly, layers and interfaces are also found in giant planets such as Saturn and Jupiter, and appear as their well-known banded structure.
Questions that are common to all fields include: why do layers form, how does a staircase evolve, how to model transport across a staircase, and what impact this has on the global evolution of the system which hosts the staircase.

The goal of this BIRS workshop will be to engage scientists (astrophysicists, oceanographers, applied mathematicians) in learning about recent research progress in answering such questions in these physically distinct, but mathematically intimately related fields. By promoting pedagogy, and the training of young researchers to think in a mathematical and multidisciplinary way from the beginning, we hope to promote outside-the-box" scientific inquiry, and from there, substantial progress in understanding these complex systems.

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.