Bitangents of tropical plane quartic curves
  We study smooth tropical plane quartic curves and show that they satisfy certain properties analogous to (but also different from) smooth plane quartics in algebraic geometry. For example, we show that every such curve admits either infinitely many or exactly 7 bitangent lines. We also prove that a smooth tropical plane quartic curve cannot be hyperelliptic. 
Matt Baker, Yoav Len, Ralph Morrison, Nathan Pflueger, Qingchun Ren
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