Stability of gamma factors, I

Gamma-factors are crucial in defining root numbers satisfying 
functional equations. Stability of gamma factors plays an important 
role in proving Langlands principle of functoriality in certain cases, 
and it provides a proof of the equality of root numbers defined from 
Langlands-Shahidi method with others including those of Artin. In the 
first part of the talk, I will briefly explain why stability of gamma 
factors leads to Langlands principle of functoriality. I will also 
introduce the previous method used to prove stability of gamma 
factors.  In the second part, I will show a new method to prove the 
problem using certain orbital integrals and the Shalika germ expansion.