Bridging the Gap between Kahler and non-Kahler Complex Geometry (19w5051)
The Banff International Research Station will host the "Bridging the Gap between Kähler and non-Kähler Complex Geometry" workshop in Banff from October 27, 2019 to November 1, 2019. Our workshop intends to bring together mathematicians working in complex analytic, differential and algebraic geometry, as well as geometric PDEs, complex analysis and topology, in an attempt to make progress towards a unified classification theory of compact complex, not necessarily algebraic or even Kähler, manifolds. This is a major endeavour in modern mathematics. We will focus on two types of structures that these manifolds may support: metric structures (ways of measuring distances on these manifolds) and cohomological structures (pertaining to topological properties of the complex structure of these manifolds). Very few manifolds admit a type of metrics, called Kähler, that have many symmetries and imply cohomological properties, but most of them do not. However, large classes of manifolds support weaker types of special metrics that imply cohomological and geometric properties similar to their Kähler counterparts. Our understanding of not necessarily Kähler manifolds remains patchy at the moment despite recent major progress. Our workshop will focus on the relations between metric and cohomological properties of compact complex manifolds that resemble Kähler manifolds to some degree.
