During the period AY2019-2022, my research activities were centered in the area of complex differential geometry. This research area will still be my focus in the next few academic years.

My research achievements during the past three years are summarized as follows:

1. In collaboration with Professor Jun-Muk Hwang of KIAS, I studied problems related to volumes of analytic varieties. We obtained sharp lower bound for volumes of analytic curves in tubular neighborhoods of the diagonal of quotients of polydisks. A joint paper (with Professor Jun-Muk Hwang) based on this result has just been published in Journal of Geometric Analysis in July 2020 (Volume 30, Issue 3, 2326-2339). https://doi.org/10.1007/s12220-017-9849-5

2. In collaboration with my former PhD student Dr. Colin Tan (currently Lecturer at SUTD), I have studied certain integral operators concerning Hermitian algebraic functions and obtained some interesting result in this direction. Our joint paper titled "Eventual Positivity of Hermitian Algebraic Functions and Associated Integral Operators" was published in Chinese Annals of Mathematics Ser. B (Volume 41, no.6, 967-988) in December 2020.

3. Colin Tan and I also obtained effective estimates concerning the eventual positivity of Hermitian algebraic functions, in terms of the geometric data involved. Our joint paper titled "Effective geometric Hermitian Positivstellensatz" was published in Journal of Geometric Analysis in printed form (Volume 31, no.2, 2105-2151) in 2021. https://doi.org/10.1007/s12220-019-00334-9

4. In collaboration with Professor Sai-Kee Yeung of Purdue University, I studied hyperbolicity properties of the moduli spaces of log-canonically polarized manifolds. Our joint paper titled "Hyperbolicity of moduli spaces of log-canonically polarized manifolds" based on this study was published in Journal of Geometric Analysis in printed form (Voulme 31, no.3, 2941-2969) in 2021. https://doi.org/10.007/s12220-020-00380-8