Recent Progress on Some Problems in Several Complex Variables and Partial Differential Equations

Problems on the Monge-Ampere equation in the plane by C. Anedda and G. Porru Global solvability for a special class of vector fields on the torus by A. P. Bergamasco and P. L. D. da Silva Deformation in the large of some complex manifolds, II by F. Catanese and P. Frediani Gradient Kahler-Ricci solitons and complex dynamical systems by A. Chau and L.-F. Tam On the summability of formal solutions for a class of nonlinear singular PDEs with irregular singularity by H. Chen, Z. Luo, and C. Zhang Upper bounds on the slope of a genus 3 fibration by Z. Chen and S.-L. Tan The mean curvature equation in pseudohermitian geometry by J.-H. Cheng Moment results for the Heisenberg group interpreted using the Weyl calculus by W. M. Eby The cohomology of vector bundles on general non-primary Hopf manifolds by N. Gan and X.-Y. Zhou Gevrey regularity in time for generalized KdV type equations by H. Hannah, A. A. Himonas, and G. Petronilho An Alexandrov type theorem for Reinhardt domains of $\mathbb{C}^2$ by J. Hounie and E. Lanconelli The quantitative estimate of unique continuation and the cost of approximate controllability for coupled parabolic systems by L. Lei, G. Wang, and L. Zhang Complete invariant of a family of strongly pseudoconvex domain in $A_1$-singularity: Bergman function by H. S. Luk, S. S.-T. Yau, and W. Zang Anisotropic blowup and compactification by G. A. Mendoza Planar complex vector fields and infinitesimal bendings of surfaces with nonnegative curvature by A. Meziani Bergman metric on Teichmuller spaces and moduli spaces of curves by S.-K. Yeung.