My research involves nonlinear PDEs in complex geometry. For those who wish to learn this topic, here are some great references:
Complex Monge Ampere Equations, D. H. Phong, Jian Song, J. Sturm
The Dirichlet problem for nonlinear second order elliptic equations, III: Functions of the eigenvalues of the Hessian, L. Caffarelli, L. Nirenberg, J. Spruck
On the Ricci Curvature of a Compact Kähler Manifold and the Complex Monge-Ampère Equation, S. T. Yau (1978)
An Introduction to the Kähler-Ricci Flow, Sebastien Boucksom, Philippe Eyssidieux, Vincent Guedj
Canonical metrics in Kähler geometry, Gang Tian
An Introduction to Extremal Kähler Metrics, Gábor Székelyhidi
Fully non-linear elliptic equations on compact Hermitian manifolds, Gábor Székelyhidi
The Monge-Ampère equation for (n-1)-plurisubharmonic functions on a compact Kähler manifold, Valentino Tosatti, Ben Weinkove.
Feel free to contact me for more specific references.
Here is the list of my papers: ArXiv