Research

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

  • 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. https://doi.org/10.1016/j.aim.2024.109627
  • 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 and Computational Geometry (2022). doi.org/10.1007/s00454-021-00362-9
  • Diane Maclagan and Josephine Yu. Higher Connectivity of Tropicalizations. Mathematische Annalen, 2021. 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. https://doi.org/10.1016/j.aim.2021.107677. arXiv:1907.08545. 
  • 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 (with Charles Wang) arXiv:1707.04581. 
  • Anton Leykin and Josephine Yu. Beyond Polyhedral Homotopies. arxiv:1706.03520. Journal of Symbolic Computations 91 (2019), 173-180. https://doi.org/10.1016/j.jsc.2018.06.019
  • Fatemeh Mohammadi, Caroline Uhler, Charles Wang, and Josephine Yu. Generalized Permutohedra from Probabilistic Graphical Models. SIAM J. Discrete Math., 32-1 (2018), 64–93. Talk at SIAM AG17.
  • Ngoc Mai Tran and Josephine Yu. Product-Mix Auctions and Tropical Geometry (with Ngoc Mai Tran), arXiv:1505.05737. Mathematics of Operations Research (2019). https://doi.org/10.1287/moor.2018.0975
  • 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.
  • Stable Intersections of Tropical Varieties (with Anders Jensen). Journal of Algebraic Combinatorics 43, 1 (2016), 101-128. (publisher, arXiv)
  • Computing tropical curves via homotopy continuation (with Anders Jensen and Anton Leykin). Experimental Mathematics 25 (2016) no. 1, 83-93.
  • Tropicalizing the Positive Semidefinite Cone. Proceedings of the American Mathematical Society 143 (2015), 1891-1895.
  • Symmetric Alcoved Polytopes (with Annette Werner). The Electronic Journal of Combinatorics 21(1) (2014), 1-20
  • Computing Tropical Resultants (with Anders Jensen), Journal of Algebra 387 (2013), 287-319.
  • Linear Systems on Tropical Curves (with Christian Haase and Gregg Musiker), Mathematische Zeitschrift 270 (2012) no. 3-4, 1111-1140.
  • An Implicitization Challenge for Binary Factor Analysis (with Maria Angelica Cueto and Enrique A. Tobis), Journal of Symbolic Computation 45 (2010) 1296 –1315, special issue for MEGA 2009. (Extended abstract presented at MEGA 2009 in Barcelona). Website.
  • On a parameterization of positive semidefinite matrices with zeros (with Mathias Drton), SIAM Journal on Matrix Analysis and Applications 31 (2010), no.5, 2665–2680.
  • The space of tropically collinear points is shellable (with Hannah Markwig). Collectanea Mathematica 60, 1 (2009), 63-77.
  • Tropical implicitization and mixed fiber polytopes (with Bernd Sturmfels), 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.
  • The hyperdeterminant and triangulations of the 4-cube (with Peter Huggins, Bernd Sturmfels, and Debbie Yuster), Mathematics of Computation 77 (2008) 1653-1679. Some data files.
  • Affine buildings and tropical convexity (with Michael Joswig and Bernd Sturmfels), Albanian Journal of Mathematics 1 (2007), 187-211.
  • Representing tropical linear spaces by circuits (with Debbie Yuster), Proceedings of FPSAC 2007.
  • The Newton polytope of the implicit equation (with Bernd Sturmfels and Jenia Tevelev). Moscow Mathematical Journal 7 (2007), 327–346.
  • Tropical polytopes and cellular resolutions (with Mike Develin), Experimental Mathematics 16:3 (2007), 277-291.
  • Tropical convexity via cellular resolutions (Erratum) (with Florian Block), Journal of Algebraic Combinatorics 24, 1 (2006), 103–114.
  • The EM algorithm for hidden markov models (with Ingileif Hallgrímsdóttir and R. Alexander Milowski), Chapter 12, Algebraic Statistics for Computational Biology, edited by Lior Pachter and Bernd Sturmfels. Cambridge University Press (2005).
  • Classification of six point metrics (with Bernd Sturmfels), Electronic Journal of Combinatorics 11 (2004) R44. Website.
  • Non-commutative matrix integrals and representation varieties of surface groups in a finite group (with Motohico Mulase), Annales de L’Institut Fourier 55, 6 (2005), 2161–2196.
  • A generating function of the number of homomorphisms from a surface group into a finite group (with Motohico Mulase), math.QA/0209008.

Other Writings

  • The EM algorithm for hidden markov models (with Ingileif Hallgrímsdóttir and R. Alexander Milowski), Chapter 12, Algebraic Statistics for Computational Biology, edited by Lior Pachter and Bernd Sturmfels. Cambridge University Press (2005). 
  • 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.

Computation