**Research**

My research interests are in the areas of
number theory and its applications. Number theory has very rich applications,
such as Cryptography, and interaction of ideas across such diverse fields as
analysis, algebra, geometry and representation theory, now even quantum mechanics
and data science. For instance, there are more and more fascinating
collaborations among physicists pursuing the implications of quantum chaos and
number theorists attracted by Riemann Hypothesis, one of the deepest problems
in mathematics.

Recently, I am interested in studying the
interactions between data science and number theory. For instance, we can apply
the method in data mining to the computational aspect of number theory
problems. On the other hand, in data analysis, the discrete structures of big
data can be well represented by p-adic number systems
and p-adic numbers have many powerful applications on
data analysis and data clustering.

I am also interested in Applied Math related
with biomathematics. Currently, we are working on some projects, which study
the clustering analysis of microRNA and mRNA expression data using various
techniques from graph theory, number theory, statistics and data mining, etc.

**Publications and preprints**

- The
Quantum Variance on the Modular Surface, joint with Peter Sarnak, accepted by Annales scientifiques de l'ENS.

- Quantum
Variance on Maass-Hecke Cusp Forms, Comm. in
Math. Phy., 475- 514, Vol.
297, 2010.

- Quantum Variance on Maass-Hecke Cusp Forms, PhD thesis, Advisor: Wenzhi Luo, Ohio State
University, 2009.

- Clustering Analysis of
microRNA and mRNA Expression Data from TCGA, joint with Lizhong
Ding, etc., submitted.

- Optimal Cluster Detection of
A Certain Directed Edge-weighted Bipartite Graph, joint with Cheng Zhao, etc.,
preprint.

- Non-Gaussian Distribution of
Higher Moments of Matrix Elements, preprint.

- A Large Sieve Type
Inequality and Its Applications on Waring-Goldbach
Problem, preprint.

- Visible Points in Lattice
Parallelograms, joint with Mizan Khan, preprint.

- Clustering Analysis of
Bipartite Graph and Markov Matrix, joint with Cheng Zhao, in progress.