Yoav Len, Department of Combinatorics & Optimization, University of Waterloo
"Tangent lines and the equation 28=7 x 4"
I will discuss algebraic and combinatorial aspects of tangent lines to curves. As shown by Plücker in the 19-th century, every smooth plane quartic curve has 28 lines that are tangent at two points, namely, bitangents. The count hides reach combinatorics, and is related to other phenomenas such as lines on a cubic surface, double covers of curves, and theta characteristics. As I will show, a similar statement holds in tropical geometry: every tropical plane quartic admits 7 bitangent lines. I will begin with a short introduction to tropical geometry, and explain how to count the bitangents to a quartic. While the proof is purely combinatorial, this is more than just an analogy: each of these tropical lines can be traced back to 4 algebraic lines. I will not assume any knowledge in algebraic or tropical geometry.
MC 5403