Stable varieties with a twist / Dan Abramovich, Brendan Hassett -- Basic properties of log canonical centers / Florin Ambro -- Burniat surfaces I: fundamental groups and moduli of primary Burniat surfaces / Ingrid Bauer, Fabrizio Catanese -- Minimal models, flips and finite generation: a tribute to V.V. Shokurov and Y.-T. Siu / Caucher Birkar, Mihai Paun -- Remarks on an example of K. Ueno / Frédéric Campana -- Special orbifolds and birational classification: a survey / Frédéric Campana -- Birational geometry of threefolds / Jungkai Alfred Chen -- Emptiness of homogeneous linear systems with ten general base points / Ciro Ciliberto, Olivia Dumitrescu, Rick Miranda, Joaquim Roé -- Finite generation of adjoint rings after Lazic: an introduction / Alessio Corti -- Log canonical thresholds on varieties with bounded singularities / Tommaso de Fernex, Lawrence Ein, Mircea Mustaţă -- Brill–Noether geometry on moduli spaces of spin curves / Gavril Farkas -- On the bimeromorphic geometry of compact complex contact threefolds / Kristina Frantzen, Thomas Peternell -- Introduction to the theory of quasi-log varieties / Osamu Fujino -- On Kawamata’s theorem / Osamu Fujino -- Remarks on the cone of divisors / Yujiro Kawamata -- p-elementary subgroups of the Cremona group of rank 3 / Yuri Prokhorov.

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Fascinating and surprising developments are taking place in the classification of algebraic varieties. Work of Hacon and McKernan and many others is causing a wave of breakthroughs in the Minimal Model Program: we now know that for a smooth projective variety the canonical ring is finitely generated. These new results and methods are reshaping the field. Inspired by this exciting progress, the editors organized a meeting at Schiermonnikoog and invited leading experts to write papers about the recent developments. The result is the present volume, a lively testimony of the sudden advances that originate from these new ideas. This volume will be of interest to a wide range of pure mathematicians, but will appeal especially to algebraic and analytic geometers.