The Baum-Connes conjecture for real reductive groups - Parts 9 & 10/10 | Vidéo

The Baum-Connes conjecture for real reductive groups - Parts 9 & 10/10

Appears in collection : 2025 - T1 - Representation theory and noncommutative geometry

Part 9 - Banach modifications of the gamma element

The problem with Banach convolution algebras from the point of view of representation theory. The problem with tensor products and unconditional norms. Unconditional norms. Karoubi density. Reduction of the Baum-Connes conjecture to $\gamma=1$. A further technical reduction. The rapid decay property for the Harish-Chandra Schwartz algebra.

Part 10 - Rapid decay property and Lafforgue’s proof of the Baum-Connes conjecture

The gamma element from Witten’s perturbation of the de Rham complex. Transfer to weighted $L^2$ spaces. A homotopy from the gamma element to 1, almost. Putting everything together.