Explore a mathematical seminar talk that delves into the fascinating relationship between the geometry of Bun_G and two-dimensional conformal field theory. Learn about conformal blocks, a fundamental concept in 2D conformal field theory, and their derived versions. Examine the specialized case of Kac-Moody Lie algebra and its maximal integrable quotient (WZW model), understanding how their conformal blocks connect to Bun_G geometry. Discover how the WZW model's conformal blocks space relates to the cohomology of the "non-abelian theta functions" line bundle on Bun_G, with particular attention to a refined version of Bun_G uniformization. Delivered by Nick Rozenblyum on May 3rd, 2023, this advanced mathematics presentation offers deep insights into the intersection of geometric and conformal field theories.