# Bi-annual Algebraic and Tropical
Meetings of

Brown and YaLE

(BATMOBYLE)

Fall 2019 @ Brown

November 15, 2019

The BATMOBYLE is a vehicle for bringing together the algebraic and
tropical geometry groups of Brown and neighboring institutions for a
biannual day of talks alternating between the participating
universities.

Abstracts
Sebastian Bozlee (Colorado) -- Contractions of logarithmic curves

TBA

Dave Jensen (Kentucky) -- Linear systems on general curves of fixed gonality

The geometry of an algebraic curve is governed by its linear systems. While many curves exhibit bizarre and pathological linear systems, the general curve does not. This is a consequence of the Brill-Noether theorem, which says that the space of linear systems of given degree and rank on a general curve has dimension equal to its expected dimension. In this talk, we will discuss a generalization of this theorem to general curves of fixed gonality. Our focus will be on an approach using tropical and combinatorial methods, but we will also discuss an independent proof, due to H. Larson. This is joint work with Kaelin Cook-Powell and Dhruv Ranganathan, based on prior work of Nathan Pflueger.

Max Kutler (Kentucky) -- The motivic zeta function of a matroid

We associate to any matroid a motivic zeta function. If the matroid is representable by a complex hyperplane arrangement, then this coincides with the motivic Igusa zeta function of the arrangement. We show that this zeta function is rational and satisfies a functional equation. Moreover, it specializes to the topological zeta function introduced by van der Veer. We compute the first two coefficients in the taylor expansion of this topological zeta function, answering two questions of van der Veer. This is joint work with David Jensen and Jeremy Usatine.

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