Explore the intricacies of two fundamental conjectures in mathematics through this 54-minute lecture by Wolfgang Lück at the Hausdorff Center for Mathematics. Delve into a comparative analysis of the Baum-Connes Conjecture and the Farrell-Jones Conjecture, examining their similarities, differences, and implications in the field of algebraic topology and geometric group theory. Gain insights into the mathematical frameworks underlying these conjectures and their significance in advancing our understanding of complex mathematical structures.