Department of Mathematics - Algebra and Geometry Seminar - Stability conditions: from curve to hyperkaehler manifolds (I & II)

In these lectures we will review the basic material about stability conditions and focus on examples. We will start reviewing the simplest example given by algebraic curves and illustrate how this allows us to move to higher dimensions passing through the case of noncommutative surfaces. The goal is to illustrate how to construct stability conditions on special hyperkaehler manifolds which are Hilbert schemes of points on special K3 surfaces and to apply this to the geometry of hyperkaehler manifolds. The new results are a joint work in progress with Chunyi Li, Emanuele Macri', Alex Perry and Xiaolei Zhao.