Explore the mathematical concept of L^2 cohomology of buildings in this lecture presented by Tadeusz Januszkiewicz from IMPAN and the University of Wrocław, Poland. Delve into the intricate relationships between geometric structures and their associated cohomology theories, focusing on the specific case of buildings. Gain insights into the applications of L^2 cohomology in the study of infinite groups and their geometric representations. Examine the methods and techniques used to analyze the cohomological properties of these complex mathematical objects, and understand their significance in modern algebraic and geometric topology.