This is a workshop on some recent analytic and algebraic interplay in the geometry of complex algebraic varieties. One emphasis will be put on the geometry of the (possibly infinite dimensional) automorphism Lie group of such a variety with such questions as the linearizability of actions on affine spaces by algebraic tori, positive entropy, the Tits alternative for lattices in such Lie groups and the (volume) density property of a complex algebraic/analytic variety. The common aim is to look for further invariants that one expects to be analytically inspired for distinguishing algebraic/analytic varieties.