These are my most current research interests:
· Number Theory and Ergodic Theory
1. Oscillating sequences, MMA and MMLS flows and Sarnak's conjecture (with Aihua Fan). Erg. Th. & Dyn. Sys., Published Online March 14, 2017.
· Complex Dynamics
1. A framework towards understanding the characterization of holomorphic maps (with an Appendix on transcendental functions written with Tao Chen and Linda Keen). Frontiers in Complex Dynamics, March 2014, Princeton University Press, 235-253.
1. Bounded geometry and families of meromorphic functions with two asymptotic values (with Tao Chen and Linda Keen). The Proceedings of the Six International Congress of Chinese Mathematicians, Higher Education Press and International Press, Beijing–Boston, ALM37, Vol II (2016), 343-362.
2. Bounded geometry and characterization of some transcendental maps (with Tao Chen and Linda Keen). Indiana University Mathematics Journal, Math. J. 66 (2017), 1537-1571.
3. Cycle doubling, merging and renormalization in the tangent family (with Tao Chen and Linda Keen). arXiv:1708.01808v1.
4. Geometrization of sub-hyperbolic semi-rational branched coverings (with Tao Cheng). arXiv1207.1292.
· Quasiconformal Mappings and Teichmüller Spaces
1. Teichmüller spaces and tame quasiconformal motions (with Sudeb Mitra, Hiroshige Shiga, and Zhe Wang). Tohoku Mathematical Journal, accepted 2016 and to appear on Vol. 71, no. 1, March 2019.
2. Variation of moduli under continuous motions (with Sudeb Mitra). Proceedings of the 6th Ahlfors-Bers Colloquium. Contemporary Mathematics, Vol. 696 (2017), 205-214.
3. Monodromy, liftings of holomorphic maps, and extensions of holomorphic motions (with Sudeb Mitra). Submitted Preprint.
· Metric Entropy in Smooth Dynamical Systems
1. Infimum of the metric entropy of hyperbolic attractors with respect to the SRB measure (with Huyi Hu and Miaohua Jiang). Discrete and Continuous Dynamical Systems, Vol. 22, No. 1&2 (2008), 215–234.
2. Infimum of the metric entropy of volume preserving Anosov systems (with Huyi Hu and Miaohua Jiang). Discrete and Continuous Dynamical Systems, Volume 37 (2017), No. 9, 4767-4783.
3. Infimum of metrtic entropy and the Boole map. Preprint.
· Applications of Quasiconformal Mappings and Teichmüller Theory to Dynamical Systems
1. An introduction to geometric Gibbs theory. Dynamics, Games and Science, CIM Series in Mathematical Sciences, Vol. 1, Springer-Verlag, 2015, 327-339.
2. Symmetric invariant measures. Contemporary Mathematics, AMS, Vol. 575, 2012, 211-218.
3. Simultaneous uniformization for uniformly quasisymmetric circle dynamical systems (with Fred Gardiner). Dynamical Systems, Vol. 30 (2015), No. 4, 543–565.
5. Bers complex manifold structure on circle diffeomorphisms. Submitted Preprint.
· Applications of Dynamical Systems to Teichmüller Theory
If you are interested in a complete list of my publications and my co-authors, please go to the list of publications.