“On the topology of aspherical complex projective manifolds and related questions’'

I will report on recent progress on various open problems involving aspherical complex projective manifolds, including the Singer-Hopf conjecture and the Bobadilla-Kollar conjecture. The first part of the talk will be more informal, stating the main problems, historical developments, and some of the recent results. The second part will be devoted to introducing the main tools and giving some technical details on the proofs of the recent results.