Algebra Seminar

11/20/2019 - 2:00pm to 3:00pm
745 POT
Speaker(s) / Presenter(s): 
Harry Richman, University of Michigan

Title: Weierstrass points on a tropical curve

Abstract: The set of (higher) Weierstrass points on an algebraic curve of genus g > 1 is an analogue of the set of N-torsion points on an elliptic curve. As N grows, the torsion points "distribute evenly" over a complex elliptic curve. This makes it natural to ask how Weierstrass points distribute, as the degree of the corresponding divisor grows. We will explore how Weierstrass points behave on tropical curves (i.e. graphs with edge lengths), and explain how their distribution can be described in terms of electrical networks. Knowledge of tropical curves will not be assumed, but knowledge of how to compute resistances (e.g. in series and parallel) will be useful.

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