Singular tropical hypersurfaces

The study of singularities and singular varieties has been an important issue in tropical geometry from the very beginning, for example, the Mikhalkin's correspondence theorem deals with nodal plane tropical curves. In the talk we address the geometry of higher-dimensional singular tropical hypersurfaces and show that even in the case of one singularity one encounters
some unexpectedly interesting geometric phenomena involving combinatorics of lattice polytopes and metric geometry. Joint work with Hannah and Thomas Markwig.