The mathematics department at Johns Hopkins University will host a conference from March 22-26, 2017, to be organized around significant recent developments in the study of local zeta functions and the arithmetic of moduli spaces. These research areas have applications to cryptography and to mathematical physics (string theory and gauge theory). One goal of the conference is to bring together researchers in these two areas so that they will constructively interact. A second goal is to encourage young researchers to participate in these developments. A significant portion of NSF funding will be used to fund the travel and housing of junior participants (e.g. graduate students and postdocs).
The study of local zeta functions has undergone a dramatic revolution thanks to the introduction of motivic local zeta functions in the mid-1990s. This has led to many important developments that will be discussed at the conference, including (among others) bounds for heights of rational points on algebraic varieties, connections with model theory, and connections with the Langlands program. The above is closely entwined with the emerging study of motives associated to low genus curves and their Jacobians, and relations with Siegel modular forms. The conference will also explore connections with birational geometry of moduli of abelian varieties of low dimension. The conference will feature 22 invited lectures over five days.