Spectral Geometry: Theory, Numerical Analysis and Applications (18w5090)

The Banff International Research Station will host the "Spectral Geometry: Theory, Numerical Analysis and Applications" workshop from July 1st to July 6th, 2018.

The discipline of spectral geometry holds its roots in classical mathematics but continues to be a vibrant area of research among mathematicians and engineers. The basic approach in spectral geometry is to study shapes through the lens of differential operators, e.g. those governing the propagation of heat or waves across a volume or surface. From a theoretical standpoint, these operators encode a remarkable variety of both fine-grained and global information about shape, such as its curvature and topology. Computational systems developed in the last few years apply this unique, multiscale perspective on shape to applications in computer graphics, modeling, machine learning, medical imaging, and other disciplines. Needed to bridge the gap between theory and practice is the design of numerical analysis techniques that faithfully approximate operators from smooth spectral geometry on computational grids, meshes, boundary representations, and other computational structures for representing a shape. The first of its kind, this workshop will bring together researchers in theoretical spectral geometry, numerical analysis, and application areas with the goal of multidisciplinary progress on the remaining challenges of this discipline. Researchers in all three categories are requested to describe their work in terms that are approachable to audience members in all communities and to identify challenge problems for future collaboration. The workshop is jointly organized by faculty with expertise in each discipline: Iosif Polterovich (Professor and Canada Research Chair in Geometry and Spectral Theory, Université de Montréal), Nilima Nigam (Professor of Mathematics, Simon Fraser University) and Justin Solomon (Assistant Professor of Electrical Engineering and Computer Science, MIT). Invited attendees and speakers will be evenly divided among these groups.

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).