Wojciech J. Gajda

Any morphism of Berkovich’s nonarchimedean analytic spaces is harmonic, i.e., preserves the Laplace equation. At the level of skeleta, which are dual intersection complexes of toroidal formal models, one recovers harmonic morphisms of Z-affine “tropical” complexes. The potential theory of pluricanonical forms on such objects reveals a Riemann-Hurwitz formula for skeleta, namely the Laplacian of the different function coincides with the tropical canonical divisor. I will present some applications to arithmetic surfaces and wild quotient singularities.