Pseudodifferential Equations and Zeta Functions

The talk aims to discuss the connections between pseudodifferential equations over non-Archimedean spaces and certain zeta functions. In the first part, we review quickly the state of the art of the theory of non-Archimdean pseudodifferential equations and the motivations behind it. In the second part, we discuss briefly the connection with Igusa local zeta functions, and with p-adic spectral zeta functions.