Explore the application of Floer cohomology to birational geometry in this 46-minute lecture by Mark Mclean for the International Mathematical Union. Learn how to prove part of the cohomological McKay correspondence through Floer cohomology group calculations and discover the use of Hamiltonian Floer cohomology in demonstrating that birational Calabi-Yau manifolds share identical small quantum cohomology algebras. Delve into topics such as the definition of Floer cohomology, the cohomological McKay correspondence, Floer theoretic proofs, birational Calabi-Yau manifolds, and quantum cup product. Access accompanying presentation slides for a comprehensive understanding of these advanced mathematical concepts.