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Cristhian Garay. Personal site

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Last update: Sep '24

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Research HR
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Name: Cristhian E. Garay López (Official profile at CIMAT)
Institution: Center for Research in Mathematics (CIMAT) (office K315)
Tel: (+52) 473 732 7155 Ext: 4529
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 (2023-2024)

  • 12 Aug. Our paper Tropical initial degeneration for systems of algebraic differential equations, got accepted for publication.
  • 26 Mar. New preprint online. Matroids and semirings attached to toric singularity arrangements. arXiv eprint: 2403.1594
  • 06 Feb. New preprint online. Bitangents of real algebraic curves: signed count and constructions. arXiv eprint: 2402.03993
  • 10 Jan 2024. External participant in the Project "Existence of rational solutions in the Busemann-von Karman-Tsien boundary layer", by Carla Valencia. IBERO University, Mexico City.
  • 24 Jul. 2023. ISSAC 2025 will be held at CIMAT Guanajuato.
  • 09 May 2023. New preprint online. Infinite matroids in tropical differential algebra. arXiv eprint: 2305.04784.
  • Past news

Summary

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

Service

Seminars

Upcoming
meetings


drapeau

French connection

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

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]
  2. Combinatorics.
    1. Matroids (Coxeter, infinite): [AEGZ], [ABFG+], [EFG], [CG24]
    2. Tropical mathematics: [AGT], [FGH+20], [FGH+23], [CGL], [BFGN], [ABFG+], [EFG]
    3. Ordered structures: [CGL], [BFGN], [BFGN], [BG]
  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+]
  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. 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, https://doi.org/10.1016/j.jalgebra.2023.10.031.

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. [BFGN] L. Bossinger, S. Falkensteiner, C. Garay-López, M.-P. Noordman, Tropical initial degeneration for systems of algebraic differential equations. arXiv eprint: 2309.10761.

Submitted

  1. [BBG] T. Blomme, E. Brugallé and C. Garay. Bitangents of real algebraic curves: signed count and constructions. arXiv eprint: 2402.03993
  2. [ABFG+] F. Aroca, L. Bossinger, S. Falkensteiner, C. Garay, et.al. Infinite matroids in tropical differential algebra. arXiv eprint: 2305.04784.
  3. [BG] F. Baril and C. Garay, Tropicalization of Schemes and Sheaves. arXiv eprint: 2304.04872.
  4. [CDG+] E. Cotterill, I. Darago, C. Garay, C. Han and T. Shaska, Arithmetic inflection of superelliptic curves. arXiv eprint: 2110.04813
  5. [EFG] E. J. Elizondo, A. Fink and C. Garay, Matroids and the space of torus-invariant subvarieties of the Grassmannian with given homology class. arXiv eprint: 2112.15334

Preprints

  1. [CG24] E. Cotterill and C. Garay, Matroids and semirings attached to toric singularity arrangements. arXiv eprint: 2403.15942
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. Matroids over a scheme. Joint with A. Fink and L. Moci.

Human resources

Courses

01/24 to 05/24
08/23 to 12/23
  • Matemáticas discretas (Algebraic combinatorics). Universidad de Guanajuato.
01/23 to 05/23
  • Métodos Combinatorios en Geometría Enumerativa Real y Compleja (O). Posgrado UNAM.
  • Algebraic Geometry. Universidad de Guanajuato.
08/22 to 12/22
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
08/20 to 12/20
  • Topology (O). CIMAT
01/20 to 05/20
  • Rigid and tropical methods in Algebraic Geometry. CIMAT
08/19 to 12/19
09/12 to 08/14

Students and Postdocs

Current students

BSc
  • Crisanto Salazar (UAS, Sinaloa).
MSc
  • Saul Aranda (CIMAT, Guanajuato),
  • Jesús Morales Simons (CIMAT, Guanajuato)
PhD
Tutorial committee
  • Oscar Castañon (PhD, IM-UNAM Cuernavaca)
  • Ruby Lizbeth Almazán Calzada (PhD, FC-UNAM)
  • Marco Favela (BSc. UIA CDMX)
Moniteur
  • Omar Carbajal Bonal (MsC. CIMAT Guanajuato)
  • Luis Quijano (MsC. CIMAT Guanajuato)

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

Postdocs

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

Social

Future and ongoing events (where am I now?)

Past events

Visitors

  • Currently none.
Past visitors

Friends and collaborators

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