Explore a one-hour lecture from Oxford University's Maria Yakerson examining the algebro-geometric version of the Adams conjecture in topology. Delve into how this mathematical concept, traditionally focused on compactifications of real vector bundles on CW-complexes, can be applied to algebraic vector bundles on smooth algebraic varieties. Learn about the implications for analyzing stable homotopy groups of spheres and discover the collaborative research findings with Alexey Ananyevskiy, Elden Elmanto, and Oliver Röndigs. Part of the 2024 Program on Motivic Homotopy Theory at IAS PCMI, this advanced mathematical discussion requires foundational knowledge in algebraic geometry, algebraic topology, and homotopy theory, with additional background in Galois cohomology and étale cohomology being beneficial.