Research Interest (Broadly) 

Harmonic analysis 

Fractal geometry

Functional Analysis

Frame theory.

Tiling theory

(Specifically)

1. Fuglede conjecture and its related problems.

2. Construction of exponential bases and frames in fractals.

3. Geometric patterns in fractals. 

4. Harmonic analysis on fractals.

5. Topics in applied harmonic analysis (Gabor frames, dynamical samplings, phase retrieval, compressive sensing, etc)

Collaborators 

Working with different people has been one of the most interesting parts of a mathematicians.

Li-Xiang An (Central China Normal University)

Randolf Chung (University of Bonn, my former undergraduate research students )

Xinrong Dai (Sun Yat Sen University, Guangzhou)

Dorin Dutkay (University of Central Florida)

Luke Evans (University of Maryland, my former Master student)

Shahram Emami (UC Davis, my former Master student)

Xiaoye Fu (Central China Normal University)

Jean-Pierre Gabardo (McMaster University)

John Haussermann (University of Central Florida, former PhD student of D. Dutkay)

Xing-Gang He (Central China Normal University)

Alex Iosevich (University of Rochester)

Ka-Sing Lau (The Chinese University of Hong Kong)

Shidong Li (San Francisco State University)

Bochen Liu (National University of Taiwan)

Frederich Littmann (North Dakota State University) 

Azita Mayeli (CUNY)

Daniel Mondo (San Francisco State University, former Master student of Shidong Li)

Vignon Oussa (BridgeWater State University)

Hal Prince (San Francisco State University, my former Master student)

Hui Rao (Central China Normal University)

Sui Tang (John Hopkins University)

Yang Wang (Hong Kong University of Science and Technology)

Eric Weber (Iowa State University)

Emmett Wyman (Northwestern University)