My publications on arXiv, DBLP, Google Scholar, and MathSciNet (subscription required).

Expository Articles

• Felipe Rincón, Ngoc Mai Tran, and Josephine Yu. Tropical Combinatorics. Notices of the American Mathematical Society, 70(1), 2023
• Josephine Yu. Convex and Combinatorial Tropical Geometry. In Surveys in Combinatorics 2022,  London Mathematical Society Lecture Note Series, pp. 237-248. Cambridge University Press, 2022

Research Articles

• Abeer Al Ahmadieh, Felipe Rincón, Cynthia Vinzant, Josephine Yu. Tropicalizing Principal Minors of Positive Definite Matrices. arXiv:2410.11220
• Abeer Al Ahmadieh, May Cai, Josephine Yu. Real and Positive Tropicalizations of Symmetric Determinantal Varieties. arXiv:2409.17462
• May Cai, Kisun Lee, and Josephine Yu. Symmetric Tropical Rank 2 Matrices. arxiv:2404.08121
• Esme Bajo, Robert Davis, Jesús A. De Loera, Alexey Garber, Sofía Garzón Mora, Katharina Jochemko, Josephine Yu. Weighted Ehrhart Theory: Extending Stanley’s nonnegativity theorem. Advances in Mathematics, Volume 444, 2024.
• Grigoriy Blekherman, Felipe Rincón, Rainer Sinn, Cynthia Vinzant, Josephine Yu. Moments, Sums of Squares, and Tropicalization. arXiv:2203.06291. 
• Francesca Gandini, Milena Hering, Diane Maclagan, Fatemeh Mohammadi, Jenna Rajchgot, Ashley K. Wheeler, Josephine Yu. Toric and tropical Bertini theorems in positive characteristic. arXiv:2111.13214.
• Daniel Hathcock and Josephine Yu. On the hypergraph connectivity of skeleta of polytopes. Discrete & Computational Geometry 69.2 (2023): 593-596. doi.org/10.1007/s00454-021-00362-9
• Diane Maclagan and Josephine Yu. Higher Connectivity of Tropicalizations. Mathematische Annalen, 384, 1–14 (2022).  DOI:10.1007/s00208-021-02281-9
• Felipe Rincón, Cynthia Vinzant, and Josephine Yu. Positively Hyperbolic Varieties, Tropicalization, and Positroids. Adv. Math. 383 (2021), Paper No. 107677, 35 pp.
• Philipp Jell, Claus Scheiderer, and Josephine Yu. Real tropicalization and analytification of semialgebraic sets. International Mathematics Research Notices, Volume 2022, Issue 2, January 2022, Pages 928–958
• Charles Wang and Josephine Yu. Toric h-vectors and Chow Betti Numbers of Dual Hypersimplices arXiv:1707.04581. 
• Anton Leykin and Josephine Yu. Beyond Polyhedral Homotopies. Journal of Symbolic Computations 91 (2019), 173-180. 
• Fatemeh Mohammadi, Caroline Uhler, Charles Wang, and Josephine Yu. Generalized Permutohedra from Probabilistic Graphical Models.  SIAM J. Discrete Math., 32-1 (2018), 64–93. 
• Ngoc Mai Tran and Josephine Yu. Product-Mix Auctions and Tropical Geometry (with Ngoc Mai Tran). Mathematics of Operations Research, 44.4 (2019): 1396-1411. 
• Josephine Yu. Algebraic Matroids and Set-Theoretic Realizability of Tropical Varieties, Journal of Combinatorial Theory, Series A, 147 (2017), 41–45.
• Josephine Yu. Do most polynomials generate a prime ideal? J. Algebra 459 (2016), 468–474.
• Anders Jensen and Josephine Yu. Stable Intersections of Tropical Varieties. Journal of Algebraic Combinatorics 43, 1 (2016), 101-128.
• Anders Jensen, Anton Leykin, and Josephine Yu. Computing tropical curves via homotopy continuation. Experimental Mathematics 25 (2016) no. 1, 83-93.
• Josephine Yu. Tropicalizing the Positive Semidefinite Cone. Proceedings of the American Mathematical Society 143 (2015), 1891-1895.
• Annette Werner and Josephine Yu. Symmetric Alcoved Polytopes. The Electronic Journal of Combinatorics 21(1) (2014), 1-20
• Anders Jensen and Josephine Yu. Computing Tropical Resultants, Journal of Algebra 387 (2013), 287-319.
• Christian Haase, Gregg Musiker, and Josephine Yu. Linear Systems on Tropical Curves, Mathematische Zeitschrift 270 (2012) no. 3-4, 1111-1140.
• Maria Angelica Cueto, Enrique A. Tobis, and Josephine Yu. An Implicitization Challenge for Binary Factor Analysis, Journal of Symbolic Computation 45 (2010) 1296 –1315, special issue for MEGA 2009. (Extended abstract presented at MEGA 2009 in Barcelona). Website.
• Mathias Drton and Josephine Yu. On a parameterization of positive semidefinite matrices with zeros, SIAM Journal on Matrix Analysis and Applications 31 (2010), no.5, 2665–2680.
• Hannah Markwig and Josephine Yu. The space of tropically collinear points is shellable. Collectanea Mathematica 60, 1 (2009), 63-77.
• Bernd Sturmfels and Josephine Yu. Tropical implicitization and mixed fiber polytopes, Software for Algebraic Geometry, I.M.A. Volumes in Mathematics and its Applications, M. Stillman, N. Takayama and J. Verschelde (eds.), 148, Springer, New York, 2008, 111-132.
• Peter Huggins, Bernd Sturmfels, Debbie Yuster, and Josephine Yu. The hyperdeterminant and triangulations of the 4-cube, Mathematics of Computation 77 (2008) 1653-1679. Some data files.
• Michael Joswig, Bernd Sturmfels, and Josephine Yu. Affine buildings and tropical convexity, Albanian Journal of Mathematics 1 (2007), 187-211.
• Debbie Yuster and Josephine Yu. Representing tropical linear spaces by circuits, Proceedings of FPSAC 2007.
• Bernd Sturmfels, Jenia Tevelev, and Josephine Yu. The Newton polytope of the implicit equation. Moscow Mathematical Journal 7 (2007), 327–346.
• Mike Develin and Josephine Yu. Tropical polytopes and cellular resolutions, Experimental Mathematics 16:3 (2007), 277-291.
• Florian Block and Josephine Yu. Tropical convexity via cellular resolutions, Journal of Algebraic Combinatorics 24, 1 (2006), 103–114. (Erratum)
• Ingileif Hallgrímsdóttir, R. Alexander Milowski, and Josephine Yu. The EM algorithm for hidden markov models, Chapter 12, Algebraic Statistics for Computational Biology, edited by Lior Pachter and Bernd Sturmfels. Cambridge University Press (2005).
• Bernd Sturmfels and Josephine Yu. Classification of six point metrics, Electronic Journal of Combinatorics 11 (2004) R44. Website.
• Motohico Mulase and Josephine Yu. Non-commutative matrix integrals and representation varieties of surface groups in a finite group, Annales de L’Institut Fourier 55, 6 (2005), 2161–2196.
• Motohico Mulase and Josephine Yu. A generating function of the number of homomorphisms from a surface group into a finite group, 2002.

Other Writings

• Ph.D. Dissertation: “Combinatorial Aspects of Tropical Geometry”, 2007, UC Berkeley
• Undergrad Senior Thesis: “Graphical expansion of matrix integrals with values in a Clifford algebra”, 2003, Explorations 6, A Journal of Undergraduate Research at UC Davis.

Slides, etc.

• Convex and Combinatorial Tropical Geometry, British Combinatorial Conference, 2022
• Graphical models and generalized permutohedra (prezi), SIAM AG17, minisymposium on Algebra and Combinatorics of Graphical Models.
• Tropical Geometry in Economics, Oct 24, 2016. Algorithms and Randomness Center, Georgia Tech.
• Harmony of Groebner Bases and the Modern Industrial Society

Computation

• NumericalTropicalGeometry, a Macaulay2 package for computing tropical curves via homotopy continuation
• Implicitization Challenge
• Hyperdeterminant and triangulations of 4-cube
• Classification of six point metric spaces