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Weierstrass points on a tropical curve

Harry Richman, University of Michigan
Tuesday, October 29, 2019 - 2:30pm to 3:30pm
PDL C-36

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. finite metric graphs), 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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