On the Interface of Geometric Measure Theory and Harmonic Analysis (24w5264)


Krystal Taylor (The Ohio State University)

(Virginia Tech)

(University of British Columbia)

Ben Jaye (Georgia Tech)


The Banff International Research Station will host the “On the Interface of Geometric Measure Theory and Harmonic Analysis” workshop in Banff from June 9 - 14, 2024.

With a history dating back to Leibniz, the modern study of fractals is of interest to a broad range of scientific communities; applied applications include describing Brownian motion of a particle, turbulence in fluids, MR diffusion data, and vascularity of tumors.

The development of new tools and systematic methods to study these sets is in demand. The Fourier transform is a powerful tool in classical analysis, geometric measure theory, mathematical physics, dynamical systems, and has varied applications. The first application of Fourier transforms to fractal geometry was Kaufman's [1968] proof of one direction of Marstrand's classical projection theorem. Since, there has been substantial progress on understanding the geometry of fractal sets using Fourier analysis, and the arising problems have attracted people from diverse fields of mathematics including number theory, dynamical systems, combinatorics, and harmonic analysis. This workshop aims to set the stage for further progress on understanding the geometry of fractal sets and broader connections to harmonic analysis and other areas of mathematics.

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).