I will explain a beautiful link between differential and algebraic geometry, called the Kempf-Ness theorem, which says that the natural notions of "quotient spaces" in the symplectic and algebraic categories can often be identified. I will then introduce hyperkähler manifolds and outline how the Kempf-Ness theorem can be used to endow certain algebraic varieties with hyperkähler structures.

This seminar gives an introduction to this weeks "QGM research seminar". The seminar is meant for Master and PhD students - all are welcome.