Time: 9h,  26/2/2014

Location: Room 6, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet Cau Giay, Ha noi

Abstract: The talk will first quickly review how geometric invariant theory is used to form quotients of group actions in algebraic geometry, focusing on the actions of special linear groups on projective spaces and their subvarieties. The rest of the talk will introduce connections between such actions and two areas of much current activity. The first involves the birational geometry of moduli spaces of curves (which are a central theme of the current Moduli Workshop at VIASM): here GIT quotients give birational models that also turn out to be variant moduli spaces. The second concerns the conjectural equivalence between the existence of Kahler metrics of constant scalar curvature and the GIT notion of $K$-stability, recently verified in important new cases by Chen, Donaldson, and Sun.