A finite graph can be viewed as a discrete analogue of a Riemann surface. In fact, Baker and Norine proved a graph-theoretic analogue of the classical Riemann-Roch theorem. Moreover, it can be described by a simple game called chip-firing game. On the other hand, Tropical Geometry is relatively new area of mathematics which can transform questions about algebraic varieties into questions about polyhedral complexes. In this talk, I will first introduce chip-firing game and the Riemann-Roch theorem for finite graphs. Then I will talk about its application to tropical curves: every smooth tropical plane quartic curve admits 7 bitangent lines. This is a tropical analogue of the classical theorem of Plücker that every smooth plane quartic curve admits 28 bitangent lines. No background is necessary.

Keywords: Riemann-Roch theorem for graphs, Tropical Geometry, Bitangent lines, and chip-firing game