Title: Quotients of the polydisc with prescribed numerical invariants

Abstract: In my talk I will be interested in complex algebraic varieties with the same Betti numbers as the n-fold product of projective lines over the complex numbers. After a short motivation I will focus on certain natural sources for such varieties, namely polydisc quotients X(G)=Hn/G, where Hn denotes the n-fold product of the upper half plane and G is a discrete cocompact and torsion-free subgroup (a lattice) of the group of biholomorphic transformations of Hn. I will hint how to find examples of varieties with specified Betti numbers coming from "irreducible" lattices G and will discuss some results and open questions on quotients X(G) which are isogenous to a higher product of algebraic curves.