Research

Preprints (on arXiv)

Anticanonical tropical cubic del Pezzos contain exactly 27 lines (with Anand Deopurkar) (2019). eprints server. [Website].

Implicitization of surfaces via geometric tropicalization. (2012). eprints server.

Local tropicalizations of splice type surface singularities (with Patrick Popescu-Pampu and Dmitry Stepanov) (2023). Mathematische Annalen (77 pages) https://doi.org/10.1007/s00208-023-02755-y . eprints server.

The Milnor fiber conjecture of Neumann and Wahl, and an overview of its proof.(with Patrick Popescu-Pampu and Dmitry Stepanov). In "Essays in geometry-dedicated to Norbert A'Campo" (A. Papadopoulos, editor), 629-709. IRMA Lect. Math. Theor. Phys., 34 EMS Press, Berlin, 2023, ISBN:978-3-98547-024-2. eprints server.

Combinatorics and real lifts of bitangents to tropical quartic curves (with Hannah Markwig) (2023). Discrete & Computational Geometry 69 (3), 597-658 (2023). https://doi.org/10.1007/s00454-022-00445-1. eprints server.

Maps between thin Schubert cells and inverse limits. Appendix to Initial degenerations of Grassmannians by D. Corey. Sel. Math. New Ser. 27, Article 57 (2021) https://doi.org/10.1007/s00029-021-00679-6. eprints server.

Tropical geometry of genus two curves (with Hannah Markwig). Journal of Algebra 517(1) (2018), 457-512 10.1016/j.jalgebra.2018.08.034. eprints server. [Website].

Cremona linearizations of some classical varieties (with Ciro Ciliberto, Massimiliano Mella, Kristian Ranestad and Piotr Zwiernik). In "From Classical to Modern Algebraic Geometry: Corrado Segre's Mastership and Legacy" (G. Casnati, A. Conte, L. Gatto, L. Giacardi, M. Marchisio, A.Verra, editors), 375--408 (2016). `Trends in the History of Science' series, edited by Birkhäuser. eprints server.

How to repair tropicalizations of plane curves using modifications (with Hannah Markwig). Experimental Mathematics 25(2) (2016), 130-164, doi 10.1080/10586458.2015.1048013. eprint server.

Faithful tropicalization of the Grassmannian of planes (with Mathias Häbich and Annette Werner). Mathematische Annalen 360(1-2) (2014), 391-437, doi 10.1007/s00208-014-1037-3. eprints server.

Algebraic and Combinatorial aspects of Tropical Geometry (book edited with Erwan Brugallé, Alicia Dickenstein, Eva-Maria Feichtner and Ilia Itenberg). Contemporary Mathematics 589 (2013), Amer. Math. Soc., Providence, RI, x + 350 p.

Mixed discriminants (with Eduardo Cattani, Alicia Dickenstein, Sandra Di Rocco and Bernd Sturmfels). Mathematische Zeitschrift 274(3) (2013), 761-778, doi 10.1007/s00209-012-1095-8. eprints server.

Tropical secant graphs of monomial curves (with Shaowei Lin). Beiträge zur Algebra und Geometrie 54 (1) (2013), 383-418, doi 10.1007/s13366-012-0091-9. eprints server.

Tropical Mixtures of Star Tree Metrics. Annals of Combinatorics 16 (2) (2012), 233-251, doi:10.1007/s00026-012-0128-7. eprints server.

The maximum independent sets of de Bruijn graphs of diameter 3 (with Dustin A. Cartwright and Enrique A. Tobis). Electronic Journal of Combinatorics 18 (1) (2011), p194. Online article. eprints server.

Polyhedral geometry of Phylogenetic Rogue Taxa (with Frederick Matsen). Bulletin of Mathematical Biology 73 (6) (2011), 1202-1226. doi:10.1007/s11538-010-9556-x. eprints server.

Tropical implicitization. Ph.D. Thesis, University of California, Berkeley (2010). [pdf]

Tropical secant graphs of monomial curves (with Shaowei Lin). 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 669-680, Discrete Math. Theor. Comput. Sci. Proc., AN, Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2010.

An Implicitization Challenge For Binary Factor Analysis (with Enrique A. Tobis and Josephine Yu). Journal of Symbolic Computation 45 (12) (2010), 1296-1315. doi:10.1016/j.jsc.2010.06.011. eprints server. [website]

Geometry of the Restricted Boltzmann Machine (with Jason Morton and Bernd Sturmfels). Algebraic Methods in Statistics and Probability II (M. Viana and H. Wynn, eds.), Contemporary Mathematics, American Mathematical Society 516 (2010), 135-153. eprints server.

Some results on inhomogeneous discriminants (with Alicia Dickenstein). Proceeding of the XVI Latin American Algebra Colloquium (Colonia del Sacramento, Uruguay, August 2005), W. Ferrer Santos, G. González Sprinberg, A. Rittatore and A. Solotar eds., Biblioteca de la Revista Matemática Iberoamericana (2007), 42--61. ISBN: 978-84-611-7907-7. eprints server.

Undergraduate Thesis: Discriminantal Varieties and Multiplicities of base points (in Spanish).

Erwan Brugallé (École Polytechnique CMRL), Dustin A. Cartwright (University of Tennessee, Knoxville), Eduardo Cattani (UMass Amherst), Ciro Ciliberto (Università Roma Tor Vergata), Anand Deopurkar (Australian National University), Alicia Dickenstein (University of Buenos Aires), Sandra Di Rocco (KTH), Eva-Maria Feichtner (University of Bremen), Mathias Häbich, Ilia Itenberg (Institut de Mathémathiques de Jussieu - UMPC- Paris 6), Shaowei Lin (UC Berkeley), Hannah Markwig (Eberhard Karls Universität Tübingen), Frederick A. Matsen (Fred Hutchinson Cancer Research Center), Massimiliano Mella (Università di Ferrara), Jason Morton (Pennsylvania State University), Patrick Popescu-Pampu (Université de Lille), Kristian Ranestad (University of Oslo), Dmitry Stepanov (MIPT - Laboratory of Algebraic Geometry and Homological Algebra), Bernd Sturmfels (UC Berkeley), Enrique A. Tobis, Annette Werner (Goethe-Universität Frankfurt), Josephine Yu (Georgia Institute of Technology), Piotr Zwiernik (Universitat Pompeu Fabra).