Cristhian Garay. Personal website

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Last update: Jan '22


Research HR

Name: Cristhian E. Garay López (Official profile at CIMAT)
Institution: Center for Research in Mathematics (CIMAT) (office K315)
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



I am a CONACYT Research fellow in Mathematics at CIMAT, in the City of Guanajuato, Mexico, since may 2019.

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 Jean-Jacques Risler and Erwan Brugallé.

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.

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

Awards and distinctions


I am a co-organizer of:




My areas of interest include:
  1. Algebraic and Rigid Algebraic Geometry (Real Algebraic, Tropical Algebraic, Rigid and non-Archimedean Algebraic).
  2. Combinatorics (Matroids, Tropical mathematics).
  3. 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 (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 (2021), Elsevier. In press.

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. 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
  2. E. Cotterill, I. Darago, C. Garay, C. Han and T. Shaska, Arithmetic inflection of superelliptic curves. arXiv eprint: 2110.04813
  3. E. Cotterill, C. Garay and J. Luviano, Exploring tropical differential equations. arXiv eprint: 2012.14067.
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.

In preparation

  1. Matroids over a scheme. Joint with Alex Fink and Luca Moci.

Expository pieces

  1. Introducción a las ecuaciones diferenciales tropicales. In Spanish.

Human resources


01/22 to 05/22 Introducción a la Geometría Algebraica no Arquimedeana y Tropical (Posgrado UNAM, en línea). Temario y más información
01/21 to 05/21 Geometría de Monoides. CIMAT (a proposal)
01/20 to 05/20 Topology. CIMAT
01/20 to 05/20 Rigid and tropical methods in Algebraic Geometry. CIMAT
08/19 to 12/19 Perfectoid algebras and spaces. 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


  • Jesus Rivera (Cinvestav-IPN)


  • Javier Ruiz (UdG)
  • Víctor Torres (ESFM-IPN)

Other (tutorial committee)

  • Pedro A. Hernández (PhD, IM-UNAM)
  • Oscar Castañon (PhD, IM-UNAM)


Future and ongoing events

Past events

Friends and collaborators


  • Otto Romero (joint with Manuel González Villa).