Colloquium: p-adic strings and arithmetic

Abstract: The p-adic string worldsheet action in genus zero has a family of deformations, which turns out to be closely related to Tate's thesis. Very recently, we found that the Green's function of the p-adic string action in genus one, defined on a Tate curve, coincides with the Neron-Tate local height function. Therefore, this basic height function in arithmetic geometry acquires a physics meaning, as well as an interpretation as a Green's function of a pseudo-differential operator defined directly on the Tate curve.

Host: Yanli Song