The goal of the class is to discuss several topics in hyperkähler geometry, ranging from more differential/analytic to more algebraic.

Topics include: review of hyperkähler as a special holonomy condition, associated twistor space, hyperkähler quotients (finite and infinite dimensional), construcion of hyperkähler metrics (e.g., compact examples via Yau's solution of Calabi's conjecture, 4 dimensional gravitational instantons, hyperkähler metrics on Higgs bundles moduli spaces, etc...), algebraic constructions of hyperkähler varieties, periods and moduli of hyperkähler manifolds, degenerations, symplectic singularities.

The class will run weekly for the rest of the semester.

Lecturer: Cristiano Spotti