====== Farbod Shokrieh (Cornell) ======

====== Divisors on Tropical Curves and the Matrix-Tree Theorem ======

===== Abstract for the Combinatorics Seminar 2015 March 31 =====

An abstract tropical curve is essentially a "metric graph" (with some extra data). There is a reasonable theory of "divisors" in this setting. For example, there is a tropical analogue of the Picard group. It turns out that the combinatorics and geometry of the Picard group are intimately related to the classical Matrix-Tree Theorem. I will describe some of these connections.

If time permits I will discuss a recent generalizations to (metric) regular matroids.

No prior knowledge in the subject will be assumed.

This talk is based on joint works with M. Baker, G. Kuperberg, and A. Yang, and with Esco He and Avery St. Dizier.


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