Cristhian Garay. Personal site

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Last update: Nov '23


Research HR

Name: Cristhian E. Garay López (Official profile at CIMAT)
Institution: Center for Research in Mathematics (CIMAT) (office K315)
Tel: (+52) 473 732 7155 Ext: 4656
Address: Jalisco S/N, Col. Valenciana CP: 36023 Guanajuato, Gto, Mexico
e-mail: cristhian dot garay at cimat dot mx
CV: upon request.

Presence in the web

News (2023)


I am a CONACYT Research fellow in Mathematics at CIMAT, in the City of Guanajuato, Mexico, since may 2019. I belong to the CIMAT's Commutative Algebra and Algebraic Geometry Academic Cluster.

I studied at the Institut de Mathématiques de Jussieu (now Institut de Mathématiques de Jussieu-Paris Rive Gauche) of the Pierre and Marie Curie University (also known as UPMC, Paris 6, and now Sorbonne University) from 2008 to 2015, under the joint direction of Erwan Brugallé and Jean-Jacques Risler.

I was a member of the research team Analyse Algébrique. My PhD thesis (Tropical intersection theory, and real inflection points of real algebraic curves) can be downloaded from here.

Awards and distinctions


I am a co-organizer of:




French connection

IdRef My connection to the French research environment can be tracked with my scanR profile page.


My areas of interest include:
  1. Algebraic and Analytic (non-Archimedean) Geometry (Real Algebraic, Tropical Algebraic, Rigid Algebraic and non-Archimedean Algebraic).
  2. Combinatorics (Matroids, Infinite Matroids, Tropical mathematics).
  3. Differential and Tropical Differential Algebraic Geometry.
  4. Inflection phenomena in Algebraic Geometry.

Right now I am very interested in the third subject. You can find a comprehensive introduction to the state of the art on the subject in our recent preprint Exploring tropical differential equations, which grew up from the previous friendly introduction that can be found  here. (first version : march 2020)

More details on some of my ongoing research projects are available in my Research Gate site.


Journal articles

  1. F. Aroca, C. Garay and Z. Toghani, The fundamental theorem of tropical differential algebraic geometry. Pacific Journal of Mathematics Vol. 283 (2016), No. 2, 257-270
  2. I Biswas, E Cotterill and C. Garay, Real inflection points of real hyperelliptic curves. Transactions of the American Mathematical Society 372 (2019), no. 7, 4805-4827.
  3. E. Cotterill and C. Garay, Real inflection points of real linear series on an elliptic curve. Experimental Mathematics (Taylor & Francis, 2019).
  4. S Falkensteiner, C. Garay, M Haiech, et. al., On Initials and the Fundamental Theorem of Tropical Partial Differential Geometry. Journal of Symbolic Computation (Elsevier, 2023), ISSN 0747-7171, https://doi.org/10.1016/j.jsc.2022.08.005.
  5. E. Cotterill, C. Garay and J. Luviano, Exploring tropical differential equations. Advances in Geometry https://doi.org/10.1515/advgeom-2023-0019.
  6. P. L. del Angel, E. J. Elizondo, C. Garay, F. Zaldívar. On T-invariant subvarieties of symplectic Grassmannians and representability of rank 2 symplectic matroids over C. Journal of Algebra, Volume 640, 2024,300-325, ISSN 0021-8693, https://doi.org/10.1016/j.jalgebra.2023.10.031.

Proceedings articles

  1. S Falkensteiner, C Garay-López, M Haiech, et. al. The Fundamental Theorem of Tropical Partial Differential Algebraic Geometry, In Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation (ISSAC '20). Association for Computing Machinery, New York, NY, USA, 178-185.
  2. E. Cotterill and C. Garay, Inflection divisors of linear series on an elliptic curve. Matemática Contemporânea, Vol. 47 (2020), 73-81. Moduli Spaces in Algebraic Geometry and Applications.


  1. L. Bossinger, S. Falkensteiner, C. Garay-López, M.-P. Noordman, Tropical initial degeneration for systems of algebraic differential equations. arXiv eprint: 2309.10761.
  2. F. Aroca, L. Bossinger, S. Falkensteiner, C. Garay, et.al. Infinite matroids in tropical differential algebra. arXiv eprint: 2305.04784.
  3. F. Baril and C. Garay, Tropicalization of Schemes and Sheaves. arXiv eprint: 2304.04872.
  4. E. Cotterill, I. Darago, C. Garay, C. Han and T. Shaska, Arithmetic inflection of superelliptic curves. arXiv eprint: 2110.04813


  1. E. J. Elizondo, C. Garay and A. Fink, Matroids and the space of torus-invariant subvarieties of the Grassmannian with given homology class. arXiv eprint: 2112.15334
The index of my preprints available on arXiv is here. One more index of (different) material available on Archive Ouverte HAL (in french) is here.

Expository pieces

  1. C. Garay, Introducción a las ecuaciones diferenciales tropicales. Mixba'al, Revista Metropolitana de Matemáticas. Vol.13, No.1 (2022), p.p 11-28.
    DOI: www.doi.org/10.24275/uami/dcbi/mix/v13n1/cgaray

In preparation

  1. Bitangents of real algebraic curves: signed count and constructions. Joint with T. Blomme and E. Brugallé.
  2. Matroids over a scheme. Joint with A. Fink and L. Moci.

Human resources

Research groups

  1. Geometría de Estructuras algebraicas cercanas a anillos conmutativos. Ver más.
  2. Métodos algebraicos y tropicales para resolver ecuaciones diferenciales algebraicas. Ver más.


08/23 to 12/23 Matemáticas discretas (Algebraic Combinatorics). Universidad de Guanajuato.
01/23 to 05/23
08/22 to 12/22 Introducción a la Geometría Algebraica Real (O). Posgrado UNAM.
Temario y más información
01/22 to 05/22
  • Introducción a la Geometría Algebraica no Arquimedeana y Tropical (O). Posgrado UNAM.
    Temario y más información
  • Calculus II. Universidad de Guanajuato.
01/21 to 05/21 Geometría de Monoides. CIMAT (a proposal)
08/20 to 12/20 Topology (O). Maestría, CIMAT
01/20 to 05/20 Rigid and tropical methods in Algebraic Geometry. CIMAT
08/19 to 12/19 Perfectoid algebras and spaces (H). CIMAT
What is... a Perfectoid Space? By Bhargav Batt.
09/12 to 08/14 Temporary Teaching and Research Assistant (A.T.E.R). Faculty of Sciences, UPMC. Paris 6


Click here to access some resources for students
Past students and duties
  • Víctor Torres (ESFM-IPN)
  • Saul Aranda (UGto)
PhD Alejandro Martínez (joint with O. Lorscheid, Rijksuniversiteit Groningen)
Other (tutorial committee) Oscar Castañon (Ph.D., IM-UNAM Cuernavaca)
Sebastian Velasco Rodríguez (Bs.C., UIA, CDMX)


  • Otto Romero (Conacyt, joint with Manuel González Villa, CIMAT Guanajuato). October 2021-Present


Future and ongoing events (where am I now?)

  • Seminario DiferenciaHable en Geometría. Facultad de Ciencias, UNAM. 30 Noviembre 2023
  • Seminario (TBH), Universidad Iberoamericana. Ciudad de México, 01 Diciembre 2023
  • 8 Congreso de Investigación Científica. UNAH-VS Honduras, 3-7 Diciembre 2023.
  • Escuela Temática de Álgebra y Geometría Algebraica, CIMAT, 11-15 Diciembre 2023
Past events


  • Currently none.
Past visitors

Friends and collaborators

(O) Means Online participation. (H) Means Hybrid participation. Default is "in person".