Visiting Assistant Professor
Department of Mathematics and Statistics
Lederle Graduate Research Tower 1030
University of Massachusetts Amherst
710 N. Pleasant Street, Amherst, MA 01003
B.S., Mathematics and Yuanpei Program, Peking University , Beijing, China, 2003-2007.
Ph.D., Mathematics, The Pennsylvania State University, 2007-2012. (Advisor: Professor Yakov Pesin).
Visiting Assistant Professor, Department of Mathematics, Michigan State University, 2012-2016. (Supervisor: Professor Huyi Hu)
Visiting Assistant Professor, Department of Mathematics and Statistics, University of Massachusetts Amherst, 2016 - present. (Supervisor: Professor Hongkun Zhang )
My research interests lie in dynamical systems and ergodic theory. Currently, I am working on the theory of nonuniform and partial hyperbolicity in smooth dynamical systems, more specifically, in the following aspects:
(a) the "coexistence phenomenon" of zero and nonzero Lyapunov exponents in various smooth systems;
(b) Existence of SRB measures for some nonuniformly or partially hyperbolic systems;
(c) Stochastic properties of some hyperbolic systems, such as decay of correlations, central limit theorem, etc.I am also interested in fractal geometry and dimension theory in dynamical systems.
4. (With Huyi Hu and Yakov Pesin) The essential coexistence phenomenon in dynamics (pdf1, pdf2), in special issue "Statistical Properties of Dynamical Systems'', Dynamical Systems, an International Journal, v. 28, 2013.
6. (With Kien Nguyen) Invariance Principles for Ergodic Systems with Slowly α-mixing Inducing Base (pdf), USUZCAMP 2017. Differential Equations and Dynamical Systems, 115--126. Springer Proceedings in Mathematics & Statistics, vol 268. Springer, Cham..Huyi Hu and Yunhua Zhou) The existence of SRB measures for some hyperbolic systems on an open region, preprint.
2. (With Huyi Hu) Exponential mixing of toral extensions over certain hyperbolic skew products, preprint.
3. Statistical properties of Lie group extensions over expanding Young towers, preprint.
4. (With Fang Wang and Hong-Kun Zhang) Markov Partitions and Thermodynamic Formalism for Hyperbolic Systems with Singularities, submitted.
5. (With Hong-Kun Zhang) Coupling Lemma and Stochastic Properties for One-dimensional Expanding Maps, preprint.
I am currently teaching STAT 515 - Statistics I, Spring 2019, at Umass Amherst. Please find information on the course webpage .
Here is my full teaching list.