My research interests include fractal geometry, complex analysis, Fourier analysis, probability theory, and analytic capacity. Currently, my research focuses on the following two areas:

1. Studying some problems in classical complex analysis from the viewpoint of fractal geometry. The main focus is on the geometric and fractal properties of analytic functions on boundaries, such as the Cauchy boundary properties of fractal measures and the boundary properties of (random) lacunary series.

2. Fourier analysis on fractals. Investigating whether the L² spaces of fractal measures possess exponential function orthogonal bases, along with the corresponding Fourier series convergence problems. A central issue in Fourier analysis is the expansion of functions into trigonometric series. It is well-known that the L² spaces of Lebesgue measures on arbitrary intervals possess orthogonal bases in the form of exponential functions. For general measures, whether their L² spaces possess an exponentials orthogonal basis has long been a concern for mathematicians. In 1998, Jorgenson and Pederson discovered the first example of a singular non-atomic measure whose L² space possesses an exponentials orthogonal basis; such measures are called spectral measures. They proved that the classical one-third Cantor measure is not a spectral measure, but the 1/2n-Cantor measure is a spectral measure.