اشکال اتومورفیک فراتر از GL2: سخنرانی‌ها از مدرسه زمستانی آریزونا 2022

The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. It connects number theory, representation theory and arithmetic geometry, and other fields in a profound way. There are nevertheless very few expository accounts beyond the GL(2) case. This book features expository accounts of several topics on automorphic forms on higher rank groups, including rationality questions on unitary group, theta lifts and their applications to Arthur's conjectures, quaternionic modular forms, and automorphic forms over functions fields and their applications to inverse Galois problems. It is based on the lecture notes prepared for the twenty-fifth Arizona Winter School on “Automorphic Forms beyond GL(2)”, held March 5–9, 2022, at the University of Arizona in Tucson. The speakers were Ellen Eischen, Wee Teck Gan, Aaron Pollack, and Zhiwei Yun. The exposition of the book is in a style accessible to students entering the field. Advanced graduate students as well as researchers will find this a valuable introduction to various important and very active research areas. Cover Title page Contents Preface (Hang Xue, editor) Chapter 1. Automorphic forms on unitary groups (E. E. Eischen) Bibliography Chapter 2. Automorphic Forms and the Theta Correspondence (Wee Teck Gan) Bibliography Chapter 3. Modular forms on exceptional groups (Aaron Pollack) Bibliography Chapter 4. Rigidity method for automorphic forms over function fields (Zhiwei Yun) Bibliography Back Cover