Suggested Topics for student presentations
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Suggested References and Topics
Tropical Linear Spaces - Grassmannians - Convexity
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How to Draw Tropical Planes (Sven Herrmann, Anders Jensen, Michael Joswig, Bernd Sturmfels). arXiv link
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The tropical totally positive Grassmannian
(David Speyer, Lauren K. Williams). arXiv link
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Affine Buildings and Tropical Convexity (Michael Joswig, Bernd Sturmfels, Josephine Yu). arXiv link
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Classical varieties - reparameterizations
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A tropical approach to secant dimensions (Jan Draisma). arXiv link
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Tropically Unirational Varieties (Jan Draisma, Bart Frenk). arXiv link
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The 4x4 minors of a 5xn matrix are a tropical basis (Melody Chan, Anders N. Jensen, Elena Rubei). arXiv link
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Connection to Berkovich analytification
- The tropicalization of the moduli space of curves (Dan Abramovich, Lucia Caporaso, Sam Payne) arXiv link
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The skeleton of the Jacobian, the Jacobian of the skeleton, and lifting meromorphic functions from tropical to algebraic curves (Matthew Baker, Joseph Rabinoff). arXiv link
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Tropical geometry of moduli spaces of weighted stable curves (Martin Ulirsch) arXiv link
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Tropicalizing the space of admissible covers (Renzo Cavalieri, Hannah Markwig, Dhruv Ranganathan)
arXiv link
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Intersections - Realizability
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Stable Intersections of Tropical Varieties (Anders Jensen, Josephine Yu). arXiv link
- Piecewise polynomials, Minkowski weights, and localization on toric varieties (Eric Katz, Sam Payne). arXiv link
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Realization spaces for tropical fans (Eric Katz, Sam Payne). arXiv link
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Linear Systems - Theta Functions
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Riemann-Roch and Abel-Jacobi theory on a finite graph (Matthew Baker, Serguei Norine). arXiv link
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Specialization of linear systems from curves to graphs (Matthew Baker). arXiv link
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Tropical curves, their Jacobians and Theta functions (Grigory Mikhalkin, Ilia Zharkov). arXiv link
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Theta characteristics of tropical K4-curves (Melody Chan, Pakawut Jiradilok). arXiv link
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Linear Systems on Tropical Curves (Christian Haase, Gregg Musiker, Josephine Yu). arXiv link
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Bitangents of tropical plane quartic curves (Matt Baker, Yoav Len, Ralph Morrison, Nathan Pflueger, Qingchun Ren). arXiv link
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Tropicalization of theta characteristics, double covers, and Prym varieties (David Jensen, Yoav Len). arXiv link
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Elliptic Curves
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The j-invariant of a plane tropical cubic (Eric Katz, Hannah Markwig, Thomas Markwig). arXiv link
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Counting tropical elliptic plane curves with fixed j-invariant (Michael Kerber, Hannah Markwig). arXiv link
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Elliptic curves in honeycomb form (Melody Chan, Bernd Sturmfels ). arXiv link
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Applications
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Toric degenerations of Gr(2,n) and Gr(3,6) via plabic graphs (Lara Bossinger, Xin Fang, Ghislain Fourier, Milena Hering, Martina Lanini). arXiv link
- The Newton Polytope of the Implicit Equation (Bernd Sturmfels, Jenia Tevelev, Josephine Yu). arXiv link
- Elimination Theory for Tropical Varieties (Bernd Sturmfels, Jenia Tevelev). arXiv link
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An Implicitization Challenge for Binary Factor Analysis (Maria Angelica Cueto, Enrique A. Tobis, Josephine Yu). arXiv link
Product-Mix Auctions and Tropical Geometry (Ngoc Mai Tran, Josephine Yu). arXiv link
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