Table of Contents

Preface.- Big and nef classes, Futaki Invariant and resolutions of cubic threefolds.- Bottom of spectra and amenability of coverings.- Some remarks on the geometry of a class of locally conformally at metrics.- Analytical properties for degenerate equations.- On the existence problem of Einstein-Maxwell Kähler Metrics.- Local moduli of scalar-flat Kähler ale surfaces.- Singular Ricci flows II.- An inequality between complex Hessian measures of Hölder continuous m-subharmonic functions and capacity.- A guided tour to normalized volume.- Towards a Liouville theorem for continuous viscosity solutions to fully nonlinear elliptic equations in conformal geometry.- Equivariant K-theory and Resolution I: Abelian actions.- Arsove-Huber’s Theorem in Higher Dimensions.- From local index theory to Bergman kernel: a heat kernel approach.- Fourier-Mukai Transforms, Euler-Green Currents, and K-Stability.- The Variations of Yang-Mills Lagrangian.- Tian’s properness conjectures: an introduction to Kähler geometry.- Ancient solutions in geometric flows.- The Kähler-Ricci flow on CP2.- Pluriclosed flow and the geometrization of complex surfaces.- From Optimal Transportation to Conformal Geometry.- Special Lagrangian Equation.- Positive scalar curvature on foliations: the enlargeability.- Kähler-Einstein metrics on toric manifolds and G-manifolds.- Some Questions in the Theory of Pseudoholomorphic Curves.