Title of the course: Hyperkahler geometry
Instructor: Prof. Misha Verbitsky
Institution: Instituto Nacional de Matemática Pura e Aplicada
Dates: 9-15 September 2019
Prerequisites: Differential geometry, topology
Level: Graduate, advanced undergraduate
Abstract: Hyperkahler manifolds are manifolds with 3 complex structures satisfying quaternionic relations, and a torsion-free orthogonal connection preserving these complex structures. A number of objects  arising in hyperkahler geometry are equipped with hyperkahler structure, such as moduli of vector bundles, deformation spaces, subvarieties and so on. This allows one to speak of “hyperkahler geometry”, similar to the usual complex algebraic geometry. I would explain basic properties of hyperkahler manifolds, give some examples and prove results about subvarieties.
Language: EN