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Explore a one-hour lecture from UCLA's Alexander Merkurjev and CNRS's Federico Scavia delving into Massey products in Galois cohomology, part of the 2024 PCMI Graduate Summer School series. Learn about the profinite inverse Galois problem and discover how the Norm-Residue Theorem (Bloch-Kato Conjecture) constrains the mod p cohomology ring of absolute Galois groups. Examine the Massey Vanishing Conjecture by Minac and Tan, which proposes that all Massey products in field Galois cohomology vanish when defined. Access complementary lecture notes featuring proofs of the mod 2 fourfold Massey Vanishing Conjecture and construction demonstrations for prime p fields. Practice concepts through provided problem sets designed for graduate-level understanding of Galois cohomology. Gain insights into motivic homotopy theory's applications in algebra and algebraic geometry, with prerequisites including knowledge of algebraic geometry, algebraic topology, and homotopy theory.
