My interests focus mainly on fractal geometry and related topics, especially:

1. Topological properties of fractal sets, e.g., homeomorphism criteria between generalized Sierpinski carpets, behaviour of connected components of self-similar sets.

2. Geometric properties of fractal sets, e.g., self-embedding maps of self-similar and self-affine sets, interior of self-similar sets and their sumsets or difference sets,  Falconer’s distance conjecture.

3. Dimension theory of fractal sets, e.g., fractal dimensions (box, Hausdorff, topological Hausdorff, etc.) of fractal sets and their relationship.