Fractal Geometry in Pure and Applied Mathematics

Research presented in Grenoble, France illuminates fractal geometry’s role in pure and applied mathematics. Advances address non-Brownian diffusion, randomized Dirichlet forms, fractal graph approximations, heat diffusion across fractal boundaries, inverse problems, and Sobolev-type spaces, offering fresh insights. This volume contains the proceedings of the AMS-SMF-EMS Special Session on Fractal Geometry in Pure and Applied Mathematics, held from July 5-9, 2022, in Grenoble, France. The volume includes papers on recent developments in fractal geometry and its applications, featuring both original research and expository summaries. Key topics include non-Brownian diffusion and randomized Dirichlet forms on Sierpinski gasket-type fractals, graph approximation of such fractals, heat diffusion across fractal boundaries and inverse problems on fractal domains. Some new results are also presented regarding Sobolev-type spaces on metric measure spaces, and function spaces related to iterated fractal drums like the Weierstrass curve.