Syllabus:   A discussion of recent techniques and results and open problems involving holomorphic pluricanonical sections and jet differentials of complex manifolds.
Topics: The techniques introduced for the deformational invariance of plurigenera and the solution of a number of conjectures on optimal constants in analysis arising from such techniques. The analytic approach to the finite generation of the canonical ring and the abundance conjecture. The hyperbolicty of a generic high-degree complex hypersurface in a complex projective space and more generally the second main theorem in Nevanlinna theory for an entire holomorphic curve in a complex projective space and its counting function for a smooth complex hypersurface.