Cristhian Garay. Personal site

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Last update: May '26

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News

• 13 Apr. Our paper "Matroids and semirings attached to toric singularity arrangements" got accepted for publication. ICMAM Latin America Springer Book Series
• 31 Mar. Our paper "Minimal solutions of tropical linear differential systems" has been published in the journal Applicable Algebra in Engineering, Communication and Computing (AAECC).
• 22 Mar. Invited to the Special session on "Algebraic Geometry and Commutative Algebra", "XXV Coloquio Latinoamericano de Álgebra".
• 18 Mar. New preprint online. A Real Shafarevich Conjecture for Universal Covers.  arXiv eprint: 2603.17939
• 5 Mar. Recipient of the Volunteer Lecturer Program, Commission for Developing Countries (CDC) of the International Mathematical Union (IMU).
• Past news

Summary

I am a Secihti (former CONAHCYT, 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 both my M2 Recherche and my PhD 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. My PhD thesis (Tropical intersection theory, and real inflection points of real algebraic curves) can be downloaded from here.
I made a visit to the Vietnam Institute for Advanced Study in Mathematics (VIASM) in Hanoi, Vietnam, from October to December 2024.

Awards and distinctions

• The paper The Fundamental Theorem of Tropical Partial Differential Algebraic Geometry won the Distinguished Paper award of the International Symposium on Symbolic and Algebraic Computation (ISSAC 2020), awarded by the Association for Computing Machinery. June 2020.
• Member of the Mexican National Researchers System (S.N.I.) Level 1. July 2024 (previously July 2022).
• Our CIMPA School "Algebraic and Tropical Methods for Solving Differential Equations" won the grant Apoyo Especial "Alfonso Nápoles Gándara", from IM-UNAM, Mexico. August 2022.
• Appointed as Local Chair ISSAC 2025, a major annual conference of computer algebra and related areas. July 2023
• Mathematical Congress of the Americas 2025 (MCA)Awardee. Institute of the Mathematical Sciences of the Americas (IMSA).
• Recipient of the Volunteer Lecturer Program, Commission for Developing Countries (CDC) of the International Mathematical Union (IMU). We planned visits to the Abdus Salam School of Mathematical Science (Abdus Salam SMS), GC University in Lahore, Pakistan.
  • September 2025
  • March 2026.

• I obtained a scholarship from the program Scientific sojourns for pre-doc students. Foundation Sciences Mathématiques de Paris (FSMP). Paris, July 2011
• I was invited to speak at the Dagstuhl Seminar 16482 for the advancement of Computer Science. November 2016.

Service

• Reviewer for zbMATH Open (Reviewer ID 19663) and Mathematical Reviews (Reviewer ID 147038).
• Member of the Editor Board Journal of Prime Research in Mathematics (JPRM) (since July 2025).
  Former Member of the Editor Board Albanian Journal of Mathematics (March 2025-March 2026)
• I am a co-organizer of:

French connection

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

• Ambassador of France Alumni Mexico network,
• Member of the Red de Investigación México-Francia (Maison Universitaire Franco-Mexicaine, MUFRAMEX)
• Member of the project "Géométrie réelle, géométrie tropicale et théorie des singularités" (ECOS Nord M19M01, 2020-2024).

Research

Areas of interest

1. Algebraic and Analytic (non-Archimedean) Geometry.
   1. Algebraic Geometry: [AEGZ], [BBG], [CDG+], [EFG], [CG24]
   2. Real Algebraic: [BCG], [CG19], [BBG]
   3. Tropical Algebraic: [BCG]
   4. non-Archimedean Algebraic: [BCG]
   5. Complex and real analytic: [AG26]
2. Combinatorics.
   1. Matroids (Coxeter, infinite, valuated): [AEGZ], [ABFG+], [EFG], [CG24], [GG25]
   2. Tropical mathematics: [AGT], [FGH+20], [FGH+23], [CGL], [BFGN], [ABFG+], [EFG], [GG25]
   3. Ordered structures: [CGL], [BFGN], [BFGN], [BG], [GG25]
3. Algebraic and tropical methods to solve algebraic differential equations.
   1. Differential and Tropical Differential Algebraic Geometry: [AGT], [FGH+20], [FGH+23], [CGL], [BFGN], [ABFG+], [GG25]
4. Geometry of Algebraic Structures Close to Commutative Rings: [BG]
5. Enumerative and Inflection phenomena in Real Algebraic Geometry: [BCG], [CG19], [BBG], [CDG+]

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.

Active research groups and projects

1. Geometry of algebraic structures close to commutative rings. Details.
2. Non-Linear Algebra
3. Algebraic and tropical methods to solve algebraic differential equations.
   Currently an external participant in the Project "Existence of rational solutions in the Busemann-von Karman-Tsien boundary layer", directed by Carla Valencia. IBERO University, Mexico City. Details.

Production

Journal articles

1. [AGT] 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. DOI:https://msp.org/pjm/2016/283-2/pjm-v283-n2-p01-s.pdf
2. [BCG] 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. [CG19] E. Cotterill and C. Garay, Real inflection points of real linear series on an elliptic curve. Experimental Mathematics Volume 31, Issue 2, 506-517 (Taylor & Francis, 2019).
4. [CG20] 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.
5. [FGH+23] S Falkensteiner, C. Garay, M Haiech, et. al., On Initials and the Fundamental Theorem of Tropical Partial Differential Geometry. Journal of Symbolic Computation, Volume 115, March–April 2023, Pages 53-73 (Elsevier, 2023), ISSN 0747-7171, https://doi.org/10.1016/j.jsc.2022.08.005.
6. [CGL] E. Cotterill, C. Garay and J. Luviano, Exploring tropical differential equations. Advances in Geometry (de Gruyter 2023). https://doi.org/10.1515/advgeom-2023-0019.
7. [AEGZ] 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,
   DOI: https://doi.org/10.1016/j.jalgebra.2023.10.031.
8. [BFGN] Bossinger, L., Falkensteiner, S., Garay-López, C. et al. Tropical initial degeneration for systems of algebraic differential equations. Bol. Soc. Mat. Mex. 31, 15 (2025).
   DOI: https://doi.org/10.1007/s40590-024-00693-6
9. [EFG] E. Javier Elizondo, Alex Fink, Cristhian Garay López, Matroids and the space of torus-invariant subvarieties of the Grassmannian with given homology class, Journal of Pure and Applied Algebra, Volume 229, Issue 6, 2025.
   DOI: https://doi.org/10.1016/j.jpaa.2025.107930.
10. [CDG+] E. Cotterill, I. Darago, C. Garay, C. Han and T. Shaska, Arithmetic inflection of superelliptic curves. Michigan Math. J. 75 (2025), 675–724.
    DOI: https://doi.org/10.1307/mmj/20216152
11. [ABFG+] Aroca F, Bossinger L, Falkensteiner S, Garay López C, González-Ramírez L, Valencia Negrete C. Infinite matroids in tropical differential algebra. Canadian Mathematical Bulletin 2026;69(1):201-221.(Published online 2025:1-21)
    DOI:10.4153/S0008439525101094
12. [AGP25] Garay-López, C., Pantaleón-Mondragón, P. R. ., & Aranda, S. (2025). Monomial ideals from a semiring perspective. Dalat University Journal of Science, 15(3), 98-117.
    DOI: https://doi.org/10.37569/DalatUniversity.15.3.1514(2025)
13. [BBG25] T. Blomme, E. Brugallé and C. Garay. Bitangents of real algebraic curves: signed count and constructions. J. Eur. Math. Soc. (2025), published online first.
    DOI: 10.4171/JEMS/1716
14. [GG26] Grigoriev, D., Garay López, C. Minimal solutions of tropical linear differential systems. AAECC (2026).
    DOI: https://doi.org/10.1007/s00200-025-00722-5

Proceedings articles

1. [FGH+20] 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.

Accepted

1. [CG24] E. Cotterill and C. Garay, Matroids and semirings attached to toric singularity arrangements. ICMAM Latin America Springer Book Series arXiv eprint: 2403.15942

Submitted

1. [AFGV] Carla Valencia-Negrete, Cristhian Garay-Lopez, Marco Favela-Rodriguez and Alonso Andapia-Viveros. Tropical Geometry as a Restricted Architecture for Physics-Informed Neural Networks: Applications in Nonlinear Fluid-Structure Examples.
2. [BG] F. Baril and C. Garay, Tropicalization of Schemes and Sheaves. arXiv eprint: 2304.04872.

Preprints

1. [AG26] Rodolfo Aguilar and Cristhian Garay, A Real Shafarevich Conjecture for Universal Covers.  arXiv eprint: 2603.17939

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. Sobre la topología de las variedades algebraicas. Joint with Jesus Eduardo Morales Simons
2. Matroids over a scheme. Joint with A. Fink and L. Moci.

Human resources

Courses

Students and Postdocs

Current students

Past students and duties
Click here to access some resources for students

Postdocs

• Rodolfo Aguilar Aguilar (Sehciti). September 2025-
• Otto Romero (Conacyt, joint with Manuel González Villa, CIMAT Guanajuato). October 2021-

Social

Future and ongoing events (where am I now?)

2026

• May 18-29. CIMPA PASCA 2.0: Pan-American School in Commutative Algebra, CIMAT Guanajuato.
• June 7-12. Fundamentals and Applications of Commutative Algebra: Conference in Honor of Rafael H. Villarreal. Cinvestav, CDMX
• August. XXV Coloquio Latinoamericano de Álgebra. Lima, Peru.

Visitors 2026

• None

Friends and collaborators

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