Degenerations in Complex Geometry

Complex geometry is an active field of research that explores the interplay between algebraic geometry, differential geometry and complex analysis. Two dominant themes have emerged in complex geometry during recent decades. The first of these pose questions about the metric structure of a complex manifold and aims to find a correspondence between algebro-geometric stability conditions and the existence of canonical metrics, as predicted by a central conjecture due to Yau, Tian and Donaldson. Another dominant theme in complex geometry is centered around the Strominger-Yau-Zaslow conjecture, a conjecture about the limiting behaviour of families of Calabi-Yau manifolds, a class of Einstein manifolds that are of central importance in mirror symmetry. This conjecture predicts a structure theory for families of Calabi-Yau manifolds, in terms of special Lagrangian torus fibrations.

Degenerations play an important role in both these themes. This common feature has led to the development of techniques that are useful in the study of both problems and has been key for substantial breakthroughs. The most fruitful of these techniques is perhaps non-Archimedean pluripotential theory, which was much developed in work by Boucksom, Favre and Jonsson, and has led to important breakthroughs for both the SYZ and YTD conjectures. The conference aims to bring together experts from these important areas of research under the common theme of degenerations.