We start with a brief introduction to tropicalization of curves over a non-archimedean field. We will briefly mention the relation between the tropicalization and the Berkovich analytification due to Baker, Payne and Rabinoff. Tropicalizations that capture certain “essential” information of the Berkovich analytification are called faithful. The computational question of constructing faithful tropicalization given defining equations for the curve is still largely open. Motivated by this, we consider a weakening of the notion of faithful tropicalizations and for Mumford curves with a three-connected planar skeleton, we construct such weakly faithful tropicalizations of their canonical embeddings.
[This talk is part of a meeting of the LMS Joint Research Group in Tropical Mathematics and its Applications, http://www.maths.qmul.ac.uk/~fink/tropicalFall15.html .]