In-Person and Online Talk 

Meeting ID:  920 2195 5230     Passcode:  The three-digit integer that is the cube of the sum of its digits. 

Tate reformulated the theory of the Riemann zeta function and its functional equation as the Mellin shadow of the Fourier transform on a certain space of function on the adeles. Conjecturally, Langlands' general automorphic L-functions and their functional equation can be interpreted in the same way following a framework due to Braverman and Kazhdan with the case of standard L-function associated with automorphic representations of GL_n and the standard representation of the dual GL_n being well known and due to Godement and Jacquet. This talk is based on a work in progress jointly with Zhilin Luo in which we propose an explicit conjectural construction for the kernel of the non abelian Fourier transform for G=GL_n and arbitrary representation of the dual GL_n.