**Research**

My research interests are in the areas of
number theory and automorphic forms. Number theory
has very rich 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.

**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.

-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.