Explore the intricate connections between finite 2-complexes, Tate cohomology, and 4-manifolds in this advanced mathematical lecture delivered by Ian Hambleton from McMaster University at the Fields Institute. Delve into sophisticated algebraic topology concepts as the speaker examines how these three mathematical structures interact and influence each other. Gain insights into the geometric and topological properties of 4-dimensional manifolds through the lens of finite 2-complexes and cohomological methods. Discover how Tate cohomology provides powerful tools for understanding the algebraic invariants of these geometric objects. This presentation forms part of the Algebraic Topology Interactions program, offering researchers and graduate students an opportunity to engage with cutting-edge developments in modern algebraic topology and geometric topology.