Laplacians and Heat Kernels: Theory and Applications (15w5110)


(CNRS -- Ecole Polytechnique)

(Yale University)

(University of California, Davis)


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).