Perverse sheaves on semi-abelian varieties: properties and applications

Abstract: I will survey recent developments in the study of perverse sheaves on semi-abelian varieties. As concrete applications, I will discuss various obstructions on the homotopy type of complex algebraic manifolds (expressed in terms of their cohomologyjump loci), homological duality properties of complex algebraic manifolds, as well as new topological characterizations of semi-abelian varieties. (Joint work with Y. Liu and B. Wang.)