ON THE LANGLANDS PROGRAM: ENDOSCOPY AND BEYOND

This is a collection of lecture notes from the minicourses in the December 2018 Langlands Workshop: Endoscopy and Beyond. The volume combines seven introductory chapters on trace formulas, local Arthur packets, and beyond endoscopy. It aims to introduce the endoscopy classification via a basic example of the trace formula for SL(2), explore the more refined questions on the structure of Arthur packets, and look beyond endoscopy following the suggestions of Langlands, Braverman–Kazhdan, Ngo, and Altuğ. The book is a helpful reference for undergraduates, postgraduates, and researchers.

Contents:

• The Invariant Trace Formula for SL(2) (Abhishek Parab)
• Lectures on the Stable Trace Formula with Emphasis on SL₂ (Tasho Kaletha)
• Mœglin's Explicit Construction of Local A-packets (Hiraku Atobe)
• Construction of p-adic Adams–Barbasch–Vogan Packets (Hiraku Atobe)
• Orbital Integrals and Normalizations of Measures (with an Appendix by Matthew Koster) (Julia Gordon)
• Beyond Endoscopy and the Trace Formula (S Ali Altuğ)
• An Introduction to the Proposal of Braverman and Kazhdan (Zhilin Luo)

Readership: Advanced undergraduate students, graduate students and researchers interested in the Langlands program.