SFU Number Theory and Algebraic Geometry Seminar: Farbod Shokrieh

I will describe some connections between arithmetic geometry of abelian varieties, non-archimedean/tropical geometry, and combinatorics. For a principally polarized abelian variety, we show an identity relating the Faltings height and the Néron--Tate height (of a symmetric effective divisor defining the polarization) which involves invariants arising from non-archimedean/tropical geometry. If time permits, we also give formulas for (non archimedean) canonical local heights in terms of tropical invariants. (Based on joint work with Robin de Jong)