Nikon Kurnosov ( London Institute for Mathematical Sciences) – Geometry of subvarieties of holomorphic symplectic manifolds

In this talk I will focus on simply-connected holomorphic symplectic manifolds - both Kähler (hyperkähler manifolds) and non-Kähler. The only known example of the latter was constructed by Bogomolov-Guan. First, I will remind the construction of known families which are mostly based on the same idea. Then I will outline some geometry of some particular examples with its connection to G_2-manifolds and birational geometry. Later, I will speak about the subvarieties of such manifolds with the main ideas rely on the deformation theory, calibrated manifolds and Lagrangian fibrations. In particular, I will show the nonexistence of some tori in hyperkahler manifolds.