Sierpinski carpet Julia sets of holomorphic maps

Sierpinski carpet is one of the most famous fractals. As a special class of Julia sets, they appeared after the work of Milnor and Tan Lei in 1993. In this talk, we will give some examples of holomorphic maps (including rational maps and transcendental entire functions) whose Julia sets are Sierpinski carpets and study their quasisymmetric geometry, Hausdorff dimension, Lebesgue measure and etc.