Prof.Chung Pang Mok，McMaster University

Kernel of Langlands' functoriality and non-linear Poisson formulas; introduction to recent works of Laurent Lafforgue

Recently there are significant new ideas in Langlands' conjectures on
functoriality, due to Lafforgue and Ngo. Their works, which also
originated from ideas of Braverman-Kazhdan, indicate that Langlands'
problem is closely related to a conjectural generalization of
Godement-Jacquet theory and non-linear version of Poisson summation
formulas.

In these lectures we will follow Lafforgue's approach to Langlands'
functoriality, via explicit construction of kernel functions.

• Lecture one and two: Notion of kernel of Langlands functoriality
• Lecture three and four: Rankin-Selberg integrals and local L-factors.
  
• Lecture five and six: Non-linear generalization of Godement-Jacquet theory
  
• Lecture seven and eight: Conjectural generalization of Poisson summation formulas
  
• Lecture nine and ten: non-linear Poisson formulas and kernel of functoriality
• References:
  The references are from Lafforgue's homepage; the links are as follows:
  (1) His long paper: http://preprints.ihes.fr/2012/M/M-12-28.pdf
  (2) His notes on his long paper: I will follow to a large extent this materialhttp://preprints.ihes.fr/2013/M/M-13-06.pdf