Linearly saturated subvarieties on uniruled projective manifolds

In the lecture we consider the existence of G2 structures on 7-manifolds with boundary, with prescribed data on the boundary. In the first part we will review general background and theory,

We show that a foliation on a projective complex manifold is algebraic with rationally connected (closure of) leaves exactly when its minimal slope with respect to some movable class is positive.

In this talk I will present a survey of the connections between canonical metrics and random point processes on a complex algebraic variety X. When the variety X has positive Kodaira dimension,