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On Gonality-Related Graph Parameters by Benjamin Weber '21, Mathematics Senior Thesis Defense

Wed, April 28th, 2021
1:00 pm
- 1:40 pm

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On Gonality-Related Graph Parameters by Benjamin Weber '21, Mathematics Senior Thesis Defense

On Gonality-Related Graph Parameters by Benjamin Weber ’21, Mathematics Senior Thesis Defense, Wednesday, April 28, 1 – 1:40 pm, live talk can be accessed at https://williams.zoom.us/j/97617951870.

Abstract:  Tropical geometry can be thought of a set of tools that allow us to associate algebraic curves with combinatorial objects such as graphs.  In particular, we can model divisor theory on algebraic curves by playing chip-firing games on a finite graph. From this study, we can define a graph invariant called gonality, which is NP-hard to compute, that encodes information on how algebraic curves embed into higher dimensions.  In this paper, we investigate two gonality-related invariants, scramble number and a property called hyperelliptic type.  First, we prove that scramble number is also NP-hard to compute, and investigate scramble numbers over cones of graphs.  Then we introduce hyperelliptic type by providing four possible definitions and investigate which definition best models hyperelliptic-type on tropical curves.

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