Integral Geometry on Manifolds with Singularities a Microlocal Approach (25frg012)

The Banff International Research Station will host the “Integral Geometry on Manifolds with Singularities a Microlocal Approach” Focussed Research Group in Banff from August 17 - 24, 2025.

In this project, we will advance tomographic imaging methods that are related to X-ray CT, Scattering Particle Tomography, etc. From a mathematical perspective, this involves the inversion of integral transforms, where physical properties, such as density, are integrated over singular curves or surfaces with corners.

Tomographic operators that integrate over smooth curves or surfaces are relatively well understood. However, transforms integrating over singular curves or surfaces are just beginning to be studied. We will characterize the reconstructed image, paying particular attention to any artifacts which may arise due to the singular curves and surfaces, and use this information to develop techniques to mitigate against these.

Microlocal analysis lies at the intersection of partial differential equations, Fourier analysis and partial differential equations, and the group's previous experience indicates that it will be an ideal tool in tackling the above advancements in imaging.

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), and Alberta’s Advanced Education and Technology.