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. Detecting geometric patterns in fractals (e.g. Erd"os similarity conjecture)

4. Harmonic analysis on fractals.

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

Research Lecture Notes 

Restriction conjecture and Kakeya sets

Fuglede's conjecture on cyclic groups (only simple results and unfinished)

Galvin-Mycielski-Solovay's theorem

Collaborators 

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

Li-Xiang An (Central China Normal University)

Amlan Banaji  (University of Jyväskylä, Finland)

Simon Baker (Loughborough University, England)

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

Angel Cruz (my former Master's student)

Xinrong Dai (Sun Yat Sen University, Guangzhou)

Dorin Dutkay (University of Central Florida)

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

Shahram Emami (UC Davis, my former Master's student)

De-Jun Feng (The Chinese University of Hong Kong)

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)

Yeonwook Jung (UC Irvine, my former Master's student)

Mihalis Kolountzakis (University of Crete, Greece)

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

Cheuk Yin Lee (The Chinese University of Hong Kong, Shenzhen)

Shidong Li (San Francisco State University)

Bochen Liu (National University of Taiwan)

Frederich Littmann (North Dakota State University) 

Azita Mayeli (CUNY)

Yuveshen Mooroogen (University of British Columbia)

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

Vignon Oussa (BridgeWater State University)

Lekha Pirya Patil (UC Irvine, my former Master's student)

Malabika Pramanik (University of British Columbia)

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)

Ying Xiong (South China University of Technology)

Peng-Fei Zhang (ChengDu University)