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Tropical Crossing Number by Noah Cape ’25

Wed, April 9th, 2025
1:00 pm
- 1:50 pm

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Tropical Crossing Number by Noah Cape ’25, Wednesday April 9, 1:00 – 1:50pm, North Science Building 113, Wachenheim, Mathematics Thesis Defense

 

Abstract:
Tropical curves in the plane are combinatorial versions of algebraic plane curves, and can be viewed as graphs drawn in a balanced, piecewise-linear war. It was previously shown by Cartwright et al (2015) that any connected, cubic graph can be drawn in the plane as a tropical curve with some number of edge intersections. The minimum number of such intersections required to draw a given graph is known as its tropical crossing number. Before this thesis, almost nothing was known about tropical crossing number. Does there exist a graph whose tropical crossing number is 1? For any positive integer k, does there exist a graph whose tropical crossing number is k? We will answer these and many other questions about tropical crossing number, developing useful tools for the general study of this graph invariant along the way.

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