Analysis on Fractals and Graphs

This workshop will mainly deal with two trends in fractal geometry.

1. Interactions between fractals and other mathematical disciplines. One is the analysis on fractals and graphs: in particular this includes investigations on Laplace operator on fractals, the spectrum of Laplace operator on graph, PDEs on fractals and graphs, and heat kernel estimates on fractals and graphs. This is a very active field of research; significant progresses on these topics have been done in the recent years, but interesting problems still remain open. 

Another one is the multi-fractal analysis which shares lots of concepts and methods with Statistical Physics. The multi-fractal is an important tool to study the thermodynamics mechanism. The recent research focuses on the case when Gibbs measures and equilibrium states are not unique.
2. Basic problems on fractals.

Namely: the structure of self-similar and self-affine sets, the structure of the subsets of self- similar sets, embeddings and bi-Lipschitz equivalence of self-similar sets, conformal equivalence; separation properties; the structure of fixed points of IFS with overlaps; self-similar measure; intersection and projection of fractals; decomposition problems related to the Furstenberg and Marstand conjectures; tangent measures.