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

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Abstracts Ralph Morrison -- Tropical curves of genus 2:

Classically, a curve of genus 2 is a hyperelliptic curve, and can be defined by an equation y^2=f(x) where f has degree 5 or 6. However, tropicalizing a curve in this form does not in general give rise to a faithful tropicalization. Using tropical modification, I will show you how to re-embed such curves to yield faithful tropicalizations. This is joint work with Maria Angelica Cueto and Hannah Markwig.

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Ana-Maria Castravet -- Derived category of moduli spaces of pointed stable rational curves:

I will report on joint work with Jenia Tevelev on Orlov's question on exceptional collections on moduli of pointed stable rational curves and related spaces.

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Bernd Sturmfels -- Nearest Points on Toric Varieties:

This talk concerns the following optimization problem: given a data point, find its best approximation in a model that is parametrized by monomials. This algebraic complexity of this problem is given by the Euclidean distance degree of a projective toric variety. We present a formula for this degree. It extends the formula of Matsui and Takeuchi for the degree of the A-discriminant in terms of Euler obstructions. The motivation for this work is the development of our optimization problem. A key ingredient is the study of characteristic classes such as the Chern-Mather class. This is joint work with Martin Helmer.

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