Shimura Varieties and Trace Formula Seminar

Harish-Chandra established the Plancherel formula for reductive groups over local fields, in which formal degrees and Plancherel measures are key ingredients. In this talk, we give a natural extension of Langlands' conjecture, which relates Plancherel measures and local L and epsilon factors, to formal degrees. Using twisted endoscopy, we also prove the conjecture for stable discrete series of U(3) over non-archimedean local fields of characteristic zero. This is joint work with Kaoru Hiraga and Tamotsu Ikeda.