This book focuses on complex geometry and covers highly active topics centered around geometric problems in several complex variables and complex dynamics, written by some of the worlds leading experts in their respective fields.

This book features research and expository contributions from the 2013 Abel Symposium, held at the Norwegian University of Science and Technology Trondheim on July 2-5, 2013. The purpose of the symposium was to present the state of the art on the topics, and to discuss future research directions.

1. E. Bedford et al: Pseudoautomorphisms with invariant elliptic curves.- 2. B. Berndtsson: The openness conjecture and complex Brunn-Minkowski inequalities.- 3. Z. Blocki: Estimates for partial and optimal constants.- 4. J.-P. Demailly: On the cohomology of pseudoeffective line bundles.- 5. F. Forstneric and A. Alarcon: Null holomorphic curves in C^3 and applications to the conformal Calabi-Yau problem.- 6. S. Grushevsky and I. Krichever: Real-normalized differentials and the elliptic Calogero-Moser system.- 7. X. Huang and Y. Zhang: On the CR transversality of holomorphic maps into hyperquadrics.- 8. J. Merker: Rationality in differential algebraic geometry.- 9. T. Ohsawa: A Survey on Levi flat hypersurfaces.- 10. S. Yau and H. Zuo: Interplay between CR geometry and Algebraic Geometry.- 11. T. Ueda: Fatou coordinates for parabolic dynamics.- 12. S.-K. Yeung: Aspects in complex hyperbolicity.- 13. X. Zhou: A Survey on L^2 extension problem.