UBC Math Department Colloquium: Mathav Murugan

There is a well-developed theory of Sobolev spaces on metric measure spaces, stemming from the seminal works of Cheeger and Shanmugalingam in the 1990s. However, this notion does not lead to a suitable space for fractals. We develop an alternate approach to Sobolev spaces on the Sierpinski carpet, which originated in the study of diffusion on fractals. We also highlight the relevance of Sobolev spaces and the corresponding energy measures to the attainment problem for conformal dimension. This is joint work with Ryosuke Shimizu.