Igusa's program for local-global principle of forms of higher degree

In this talk, I will introduce the idea of Igusa to generalize local-global principle (Hasse principle) to forms of higher degree. This idea suggest us to have a Poisson summation formula. Igusa showed that the existence of such Poisson formula can follow by a conjecture on exponential sums modulo $p^m$. I will introduce some progress on the exponential sum conjecture and some expected results in Hasse principle may be obtained by the program of Igusa.