Advances in hyperkähler and holomorphic symplectic geometry (12w5126)
Marco Gualtieri (University of Toronto)
Jacques Hurtubise (McGill University)
Daniel Huybrechts (University of Bonn)
Eyal Markman (University of Massachusetts Amherst)
Ruxandra Moraru (University of Waterloo)
Justin Sawon (University of North Carolina)
There are two main scientific objectives. The first is to summarize and understand the recent developments and main questions within the different groups of researchers focusing on hyperkahler geometry, including the recent work on the Torelli theorem, the algebro-geometric study of holomorphic Lagrangian fibrations, and the study of hypertoric varieties. The second aim is to introduce new ideas coming from physics in the recent papers of Kapustin-Rozansky-Saulina and Gaiotto-Moore-Neitzke and to work on some of the many open questions resulting from this seminal work. Specifically, the three main questions which must be resolved are whether the categorical structure they obtain on holomorphic Lagrangians can be made mathematically precise, whether the structure can be computed in known special cases, and what impact this has on the study of holomorphic symplectic manifolds, and possibly on holomorphic Poisson manifolds.
For students and postdocs, the workshop will provide two parallel opportunities: first, to learn well-established aspects of the theory of holomorphic symplectic and hyperk"ahler manifolds, and second, to be exposed to the plethora of open questions ripe for investigation, deriving from the recent advances listed above.