Explore a 56-minute lecture by Vladimir Chernousov from the University of Alberta, delivered at the Fields Institute on April 26th, 2022. Delve into the intricate world of extended affine Lie algebras and the classification of torsors over Laurent polynomial rings. Examine the conjugacy of Cartan subalgebras and their implications in algebraic structures. Follow the speaker's journey through key concepts, including definitions, main questions, examples, and observations. Gain insights into extended Lie algebras, general definitions, and explicit descriptions. Discover the bridge between different mathematical concepts and explore natural questions arising from the discussion. Investigate the local-global principle and its application to quadratic forms. This talk is part of "The Pursuit of Symmetry: A Conference in Honour of the 80th Birthday of Robert V. Moody," offering a deep dive into advanced mathematical topics for researchers and enthusiasts in the field.