Laplacians and Heat Kernels: Theory and Applications

The Banff International Research Station will host the "Laplacians and Heat Kernels: Theory and Applications" workshop from March 22nd to March 27th, 2015.

The investigation of eigenvalues and eigenfunctions of the Laplace operator is a subject with a history of more than two hundred years. This is still a central area in mathematics, physics, engineering, and computer science and activity has increased dramatically in the past twenty years. Vibrations of a drum and propagation of sound, diffusion of molecules, migration of species, quantum states of particles, and formation of colloidal aggregates, as well as many other natural phenomena can be mathematically described by elliptic operators, with the prominent example of the Laplace operator.

When the geometry of a confining domain (e.g., a drum) is not simple, many fascinating effects can emerge. For example, the localization of some eigenfunctions in small regions of the domain was used to build highly efficient noise protective walls. Beside classical spectral expansions in mathematics, Laplacian eigenfunctions turn out to be a natural tool for a broad range of areas, e.g., data mining with fast search algorithms (e.g., Google), dimension reduction of high-dimensional datasets via spectral clustering and diffusion maps, or analysis of regional brain functions using MRI images.

In this proposed interdisciplinary 5-day workshop on Laplacian eigenvalue problems and the related heat kernels, we will bring together leading experts and young scientists in many disciplines to make further progress on understanding these fascinating problems.

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).

BIRS Scientific Director, Nassif Ghoussoub
E-mail: birs-director[@]birs.ca
http://www.birs.ca/~nassif