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Explore the geometric realization of affine Hecke algebras through equivariant K-theory in this advanced mathematical lecture. Delve into the fundamental properties of Springer resolution and Steinberg varieties while gaining an introduction to equivariant K-theory concepts. Examine the groundbreaking geometric realization of affine Hecke algebras discovered by Kazhdan-Lusztig and Ginzburg, and understand how this framework was instrumental in achieving the Deligne-Langlands classification of irreducible modules for affine Hecke algebras. Learn about the sophisticated mathematical connections between algebraic geometry, representation theory, and K-theory through detailed explanations and rigorous mathematical development. This lecture, recorded during the thematic meeting "Galois representations and automorphic forms" at the Centre International de Rencontres Mathématiques in Marseille, provides deep insights into one of the most significant developments in modern representation theory and algebraic geometry.
