Ralph Morrison: Tropical Geometry Mini-course, Part IV: Bitangent lines of tropical quartic curves

In classical algebraic geometry, a smooth plane quartic curve has 28 bitangent lines.  In this talk, I will present the corresponding result for smooth tropical plane quartic curves, which have 7 natural classes of bitangent lines.  The proof will treat the curves as both abstract and embedded objects, and will tie together the different perspectives of tropical geometry we've seen throughout the mini-course.  We will close with a discussion of relationships to classical quartic curves.  (This is based on joint work with Matthew Baker, Yoav Len, Nathan Pflueger, and Qingchun Ren.)