Appears in collection : 2025 - T1 - WS3 - Analysis on homogeneous spaces and operator algebras

This talk will be an update on the Atlas of Lie Groups and Representations project. I will describe an algorithm for computing the unitary dual of a real reductive group, and discuss our computer calculations of $E_7$ and (partially completed) $E_8$. Then I will discuss recent progress on proving Arthur's conjectures about the unitary of Arthur packets for real reductive groups. This work is joint with the members of the Atlas project - Lucas Mason-Brown, Stephen Miller, Marc van Leeuwen, Annegret Paul and David Vogan, as well as Dougal Davis and Kari Vilonen.