Explore the intricacies of G-equivariant birational geometry in three-dimensional projective space through this illuminating lecture. Delve into the complexities of finite group G actions on projective space and uncover the specific scenarios where the projective space resists G-equivariant birational transformation into fibrations of rational curves or surfaces. Gain valuable insights from Ivan Cheltsov of the University of Edinburgh as he navigates this advanced topic in algebraic geometry, offering a comprehensive analysis of the interplay between group actions and birational transformations in projective geometry.