### Curves, Graphs, and Tangent Lines

- Series
- Algebra Seminar
- Time
- Monday, April 24, 2017 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Yoav Len – University of Waterloo

I will discuss the interplay between tangent lines of algebraic and tropical curves. By tropicalizing all the tangent lines
of a plane curve, we obtain the tropical dual curve, and a recipe
for computing the Newton polygon of the dual projective curve.
In the case of canonical curves, tangent lines are closely related
with various phenomena in algebraic geometry such as double covers, theta characteristics and Prym varieties. When degenerating
them in families, we discover analogous constructions in tropical
geometry, and links between quadratic forms, covers of graphs and
tropical bitangents.